PREFACE
Excerpts
PREFACE
The study of algebra is a continuation of what the pupil has been doing for years, but it is expected that this new work will result in a knowledge of *general truths* about numbers, and an increased power of clear thinking.
PREFACE
All the differences between this work and that pursued in arithmetic may be traced to the introduction of two new elements, namely, negative numbers and the representation of numbers by letters.
PREFACE
One of these is the use of *letters to represent numbers*, and you will see in the following exercises that this change makes the solution of problems much easier.
PREFACE
Where in arithmetic did you learn the principle applied in transposing the 8?
PREFACE
instead of making a statement of what the child is to see in the illustrative example, questions are asked which shall lead him to find for himself that which he is to learn from the example.
Equations
Problems
Exercise 1
Exercise 1, problem 1
The greater of two numbers is twice the less, and the sum of the numbers is 129. What are the numbers?
Printed answer:- 43; 86.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 43, y: 86}
Exercise 1, problem 10
A house cost $2880 more than a lot of land, and five times the cost of the lot equals the cost of the house. What was the cost of each?
Printed answer:- Lot, $720; house, $3600.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{L: 720, H: 3600}
Exercise 1, problem 11
Mr. A. is 48 years older than his son, but he is only three times as old. How old is each?
Printed answer:- Mr. A, 72; son, 24.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{A: 72, s: 24}
Exercise 1, problem 12
Two farms differ by 250 acres, and one is six times as large as the other. How many acres in each?
Printed answer:- 50 A.; 300 A.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{s: 50, l: 300}
Exercise 1, problem 13
William paid eight times as much for a dictionary as for a rhetoric. If the difference in price was $6.30, how much did he pay for each?
Printed answer:- Dict., $7.20; rhet, $.90.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{r: Rational(9, 10), d: Rational(36, 5)}
Exercise 1, problem 14
The sum of two numbers is 4256, and one is 37 times as great as the other. What are the numbers?
Printed answer:- 112; 4144.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 112, y: 4144}
Exercise 1, problem 15
Aleck has 48 cents more than Arthur, and seven times Arthur’s money equals Aleck’s. How much has each?
Printed answer:- Aleck, 56; Arthur, 8.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 8, k: 56}
Exercise 1, problem 16
The sum of the ages of a mother and daughter is 32 years, and the age of the mother is seven times that of the daughter. What is the age of each?
Printed answer:- Mother, 28; daughter, 4.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{m: 28, d: 4}
Exercise 1, problem 17
John’s age is three times that of Mary, and he is 10 years older. What is the age of each?
Printed answer:- J, 15 yrs.; M, 5 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{J: 15, M: 5}
Exercise 1, problem 2
A man bought a horse and carriage for $500, paying three times as much for the carriage as for the horse. How much did each cost?
Printed answer:- Carriage, $375; horse, $125.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 125, c: 375}
Exercise 1, problem 3
Two brothers, counting their money, found that together they had $186, and that John had five times as much as Charles. How much had each?
Printed answer:- C, $31; J, $155.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{C: 31, J: 155}
Exercise 1, problem 4
Divide the number 64 into two parts so that one part shall be seven times the other.
Printed answer:- 8; 56.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 8, y: 56}
Exercise 1, problem 5
A man walked 24 miles in a day. If he walked twice as far in the forenoon as in the afternoon, how far did he walk in the afternoon?
Printed answer:- 8 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 8}
On the STU-32 (STU, rpn):
24 ENTER 2 ENTER 1 + ÷
Calculator:
+8E+0; the book prints8. Run on the calculator core at firmware628c96c.Exercise 1, problem 6
For 72 cents Martha bought some needles and thread, paying eight times as much for the thread as for the needles. How much did she pay for each?
Printed answer:- Needles, 8; thread, 64.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{n: 8, t: 64}
Exercise 1, problem 7
In a school there are 672 pupils. If there are twice as many boys as girls, how many boys are there?
Printed answer:- 224 girls; 448 boys.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{g: 224, b: 448}
Exercise 1, problem 8
Find two numbers such that their difference is 250 and one is eleven times the other.
Printed answer:- 25; 275.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 25, y: 275}
Exercise 1, problem 9
James gathered 12 quarts of nuts more than Henry gathered. How many did each gather if James gathered three times as many as Henry?
Printed answer:- H, 6 qts.; J, 18 qts.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 6, j: 18}
Exercise 1, problem None
The sum of two numbers is 60, and the greater is four times the less. What are the numbers?
Printed answer:- The numbers are 12 and 48.
- The numbers are 12 and 60.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation12solve: passes, with the problem read into an equation{x: 12, y: 60}
On the STU-32 (STU, rpn):
60 ENTER 1 ENTER 4 + ÷
Calculator:
+12E+0; the book prints12. Run on the calculator core at firmware628c96c.
Exercise 2
Exercise 2, problem 1
A man bought a hat, a pair of boots, and a necktie for $7.50; the hat cost four times as much as the necktie, and the boots cost five times as much as the necktie. What was the cost of each?
Printed answer:- Necktie, $.75; hat, $3; boots, $3.75.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{n: 0.75, h: 3, b: 3.75}
Exercise 2, problem 10
There are 120 pigeons in three flocks. In the second there are three times as many as in the first, and in the third as many as in the first and second combined. How many pigeons in each flock?
Printed answer:- 15; 45; 60 pigeons.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f1: 15, f2: 45, f3: 60}
Exercise 2, problem 11
Divide 209 into three parts so that the first part shall be five times the second, and the second three times the third.
Printed answer:- 165; 33; 11.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 165, s: 33, t: 11}
Exercise 2, problem 12
Three men, A, B, and C, earned $110; A earned four times as much as B, and C as much as both A and B. How much did each earn?
Printed answer:- A, $44; B, $11; C, $55.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{A: 44, B: 11, C: 55}
Exercise 2, problem 13
A farmer bought a horse, a cow, and a calf for $72; the cow cost twice as much as the calf, and the horse three times as much as the cow. What was the cost of each?
Printed answer:- Calf, $8; cow, $16; horse, $48.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{k: 8, c: 16, h: 48}
Exercise 2, problem 14
A cistern, containing 1200 gallons of water, is emptied by two pipes in two hours. One pipe discharges three times as many gallons per hour as the other. How many gallons does each pipe discharge in an hour?
Printed answer:- 150; 450 gal.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{s: 150, f: 450}
Exercise 2, problem 15
A butcher bought a cow and a lamb, paying six times as much for the cow as for the lamb, and the difference of the prices was $25. How much did he pay for each?
Printed answer:- Cow, $30; lamb, $5.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{c: 30, l: 5}
Exercise 2, problem 16
A grocer sold one pound of tea and two pounds of coffee for $1.50, and the price of the tea per pound was three times that of the coffee. What was the price of each?
Printed answer:- Tea, 90; coffee, 30.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{t: 90, c: 30}
Exercise 2, problem 17
By will Mrs. Cabot was to receive five times as much as her son Henry. If Henry received $20,000 less than his mother, how much did each receive?
Printed answer:- Mrs. C, $25,000; Henry, $5000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{m: 25000, h: 5000}
Exercise 2, problem 2
A man traveled 90 miles in three days. If he traveled twice as far the first day as he did the third, and three times as far the second day as the third, how far did he go each day?
Printed answer:- 30; 45; 15 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{d1: 30, d2: 45, d3: 15}
Exercise 2, problem 3
James had 30 marbles. He gave a certain number to his sister, twice as many to his brother, and had three times as many left as he gave his sister. How many did each then have?
Printed answer:- James, 15; sister, 5; brother, 10.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{j: 15, s: 5, b: 10}
Exercise 2, problem 4
A farmer bought a horse, cow, and pig for $90. If he paid three times as much for the cow as for the pig, and five times as much for the horse as for the pig, what was the price of each?
Printed answer:- Pig, $10; cow, $30; horse, $50.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{p: 10, c: 30, h: 50}
Exercise 2, problem 5
A had seven times as many apples, and B three times as many as C had. If they all together had 55 apples, how many had each?
Printed answer:- A, 35; B, 15; C, 5.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 35, b: 15, c: 5}
Exercise 2, problem 6
The difference between two numbers is 36, and one is four times the other. What are the numbers?
Printed answer:- 12; 48.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{s: 12, L: 48}
Exercise 2, problem 7
In a company of 48 people there is one man to each five women. How many are there of each?
Printed answer:- 8 men; 40 women.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{m: 8, w: 40}
Exercise 2, problem 8
A man left $1400 to be distributed among three sons in such a way that James was to receive double what John received, and John double what Henry received. How much did each receive?
Printed answer:- Henry, $200; John, $400; James, $800.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 200, j: 400, a: 800}
Exercise 2, problem 9
A field containing 45,000 feet was divided into three lots so that the second lot was three times the first, and the third twice the second. How large was each lot?
Printed answer:- 4500 ft.; 13,500 ft.; 27,000 ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 4500, y: 13500, z: 27000}
Exercise 3
Exercise 3, problem 1
In a class of 35 pupils there are 7 more girls than boys. How many are there of each?
Printed answer:- 14 boys; 21 girls.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{b: 14, g: 21}
Exercise 3, problem 10
The sum of three numbers is 56; the second is 3 more than the first, and the third 5 more than the first. What are the numbers?
Printed answer:- 16; 19; 21.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 16, b: 19, c: 21}
Exercise 3, problem 11
Divide 62 into three parts such that the first part is 4 more than the second, and the third 7 more than the second.
Printed answer:- 21; 17; 24.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 21, b: 17, c: 24}
Exercise 3, problem 12
Three men together received $34,200; if the second received $1500 more than the first, and the third $1200 more than the second, how much did each receive?
Printed answer:- $10,000; $11,500; $12,700.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 10000, b: 11500, c: 12700}
Exercise 3, problem 13
Divide 65 into three parts such that the second part is 17 more than the first part, and the third 15 less than the first.
Printed answer:- 21; 38; 6.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 21, b: 38, c: 6}
Exercise 3, problem 14
A man had 95 sheep in three flocks. In the first flock there were 23 more than in the second, and in the third flock 12 less than in the second. How many sheep in each flock?
Printed answer:- 51; 28; 16 sheep.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 51, b: 28, c: 16}
Exercise 3, problem 15
In an election, in which 1073 ballots were cast, Mr. A receives 97 votes less than Mr. B, and Mr. C 120 votes more than Mr. B. How many votes did each receive?
Printed answer:- A, 253; B, 350; C, 470 votes.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{A: 253, B: 350, C: 470}
Exercise 3, problem 16
A man owns three farms. In the first there are 5 acres more than in the second and 7 acres less than in the third. If there are 53 acres in all the farms together, how many acres are there in each farm?
Printed answer:- 17; 12; 24 A.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f1: 17, f2: 12, f3: 24}
Exercise 3, problem 17
Divide 111 into three parts so that the first part shall be 16 more than the second and 19 less than the third.
Printed answer:- 36; 20; 55.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 36, b: 20, c: 55}
Exercise 3, problem 18
Three firms lost $118,000 by fire. The second firm lost $6000 less than the first and $20,000 more than the third. What was each firm’s loss?
Printed answer:- $50,000; $44,000; $24,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 50000, b: 44000, c: 24000}
Exercise 3, problem 2
The sum of the ages of two brothers is 43 years, and one of them is 15 years older than the other. Find their ages.
Printed answer:- 14 yrs.; 29 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 29, b: 14}
Exercise 3, problem 3
At an election in which 1079 votes were cast the successful candidate had a majority of 95. How many votes did each of the two candidates receive?
Printed answer:- 492; 587 votes.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 587, b: 492}
Exercise 3, problem 4
Divide the number 70 into two parts, such that one part shall be 26 less than the other part.
Printed answer:- 22; 48.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 22, b: 48}
Exercise 3, problem 5
John and Henry together have 143 marbles. If I should give Henry 15 more, he would have just as many as John. How many has each?
Printed answer:- J, 79; H, 64.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{J: 79, H: 64}
Exercise 3, problem 6
In a storehouse containing 57 barrels there are 3 less barrels of flour than of meal. How many of each?
Printed answer:- Flour, 27 bbls.; meal, 30 bbls.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 27, m: 30}
Exercise 3, problem 7
A man whose herd of cows numbered 63 had 17 more Jerseys than Holsteins. How many had he of each?
Printed answer:- 23 Hol.; 40 Jer.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 23, j: 40}
Exercise 3, problem 8
Two men whose wages differ by 8 dollars receive both together $44 per month. How much does each receive?
Printed answer:- $18; $26.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 26, b: 18}
Exercise 3, problem 9
Find two numbers whose sum is 99 and whose difference is 19.
Printed answer:- 40; 59.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 59, y: 40}
Exercise 4
Exercise 4, problem 1
Charles and Henry together have 49 marbles, and Charles has twice as many as Henry and 4 more. How many marbles has each?
Printed answer:- C, 34; H, 15.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{c: 34, h: 15}
Exercise 4, problem 10
Divide the number 23 into three parts, such that the second is 1 more than the first, and the third is twice the second.
Printed answer:- 5; 6; 12.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{p1: 5, p2: 6, p3: 12}
Exercise 4, problem 11
Divide the number 137 into three parts, such that the second shall be 3 more than the first, and the third five times the second.
Printed answer:- 17; 20; 100.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 17, b: 20, c: 100}
Exercise 4, problem 12
Mr. Ames builds three houses. The first cost $2000 more than the second, and the third twice as much as the first. If they all together cost $18,000, what was the cost of each house?
Printed answer:- $5000; $3000; $10,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 5000, s: 3000, t: 10000}
Exercise 4, problem 13
An artist, who had painted three pictures, charged $18 more for the second than the first, and three times as much for the third as the second. If he received $322 for the three, what was the price of each picture?
Printed answer:- $50; $68; $204.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 50, s: 68, t: 204}
Exercise 4, problem 14
Three men, A, B, and C, invest $47,000 in business. B puts in $500 more than twice as much as A, and C puts in three times as much as B. How many dollars does each put into the business?
Printed answer:- A, $5000; B, $10,500; C, $31,500.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{A: 5000, B: 10500, C: 31500}
Exercise 4, problem 15
In three lots of land there are 80,750 feet. The second lot contains 250 feet more than three times as much as the first lot, and the third lot contains twice as much as the second. What is the size of each lot?
Printed answer:- 8000; 24,250; 48,500ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 8000, s: 24250, t: 48500}
Exercise 4, problem 16
A man leaves by his will $225,000 to be divided as follows: his son to receive $10,000 less than twice as much as the daughter, and the widow four times as much as the son. What was the share of each?
Printed answer:- Daughter, $25,000; son, $40,000; widow, $160,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{d: 25000, s: 40000, w: 160000}
Exercise 4, problem 17
A man and his two sons picked 25 quarts of berries. The older son picked 5 quarts less than three times as many as the younger son, and the father picked twice as many as the older son. How many quarts did each pick?
Printed answer:- Father, 14 qts.; older son, 7 qts.; younger son, 4 qts.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{F: 14, O: 7, Y: 4}
Exercise 4, problem 18
Three brothers have 574 stamps. John has 15 less than Henry, and Thomas has 4 more than John. How many has each?
Printed answer:- H, 200 stamps; J, 185 stamps; T, 189 stamps.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{H: 200, J: 185, T: 189}
Exercise 4, problem 2
In an orchard containing 33 trees the number of pear trees is 5 more than three times the number of apple trees. How many are there of each kind?
Printed answer:- 26 pear; 7 apple.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{p: 26, a: 7}
Exercise 4, problem 3
John and Mary gathered 23 quarts of nuts. John gathered 2 quarts more than twice as many as Mary. How many quarts did each gather?
Printed answer:- J, 16 qts.; M, 7 qts.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{j: 16, m: 7}
Exercise 4, problem 4
To the double of a number I add 17 and obtain as a result 147. What is the number?
Printed answer:- 65.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation65
On the STU-32 (STU, rpn):
147 ENTER 17 −
2 ÷
Calculator:
+65E+0; the book prints65. Run on the calculator core at firmware628c96c.Exercise 4, problem 5
To four times a number I add 23 and obtain 95. What is the number?
Printed answer:- 18.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation18
On the STU-32 (STU, rpn):
95 ENTER 23 −
4 ÷
Calculator:
+18E+0; the book prints18. Run on the calculator core at firmware628c96c.Exercise 4, problem 6
From three times a number I take 25 and obtain 47. What is the number?
Printed answer:- 24.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation24
On the STU-32 (STU, rpn):
47 ENTER 25 +
3 ÷
Calculator:
+24E+0; the book prints24. Run on the calculator core at firmware628c96c.Exercise 4, problem 7
Find a number which being multiplied by 5 and having 14 added to the product will equal 69.
Printed answer:- 11.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation11
On the STU-32 (STU, rpn):
69 ENTER 14 −
5 ÷
Calculator:
+11E+0; the book prints11. Run on the calculator core at firmware628c96c.Exercise 4, problem 8
I bought some tea and coffee for $10.39. If I paid for the tea 61 cents more than five times as much as for the coffee, how much did I pay for each?
Printed answer:- Tea, $8.76; coffee, $1.63.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{t: Rational(876, 100), c: Rational(163, 100)}
Exercise 4, problem 9
Two houses together contain 48 rooms. If the second house has 3 more than twice as many rooms as the first, how many rooms has each house?
Printed answer:- 15; 33 rooms.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 15, s: 33}
Exercise 5
Exercise 5, problem 1
Mary bought some blue ribbon at 7 cents a yard, and three times as much white ribbon at 5 cents a yard, paying $1.10 for the whole. How many yards of each kind did she buy?
Printed answer:- Blue, 5 yds.; white, 15 yds.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{b: 5, w: 15}
Exercise 5, problem 10
I sold three houses, of equal value, and a barn for $16,800. If the barn brought $1200 less than a house, what was the price of each?
Printed answer:- House, $4500; barn, $3300.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 4500, b: 3300}
Exercise 5, problem 11
Five lots, two of one size and three of another, aggregate 63,000 feet. Each of the two is 1500 feet larger than each of the three. What is the size of the lots?
Printed answer:- 12,000; 13,500 ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 13500, y: 12000}
Exercise 5, problem 12
Four pumps, two of one size and two of another, can pump 106 gallons per minute. If the smaller pumps 5 gallons less per minute than the larger, how much does each pump per minute?
Printed answer:- 29 gal.; 24 gal.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{L: 29, S: 24}
Exercise 5, problem 13
Johnson and May enter into a partnership in which Johnson’s interest is four times as great as May’s. Johnson’s profit was $4500 more than May’s profit. What was the profit of each?
Printed answer:- Johnson, $6000; May, $1500.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{J: 6000, M: 1500}
Exercise 5, problem 14
Three electric cars are carrying 79 persons. In the first car there are 17 more people than in the second and 15 less than in the third. How many persons in each car?
Printed answer:- 27; 10; 42.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{F: 27, S: 10, T: 42}
Exercise 5, problem 15
Divide 71 into three parts so that the second part shall be 5 more than four times the first part, and the third part three times the second.
Printed answer:- 3; 17; 51.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 3, b: 17, c: 51}
Exercise 5, problem 16
I bought a certain number of barrels of apples and three times as many boxes of oranges for $33. I paid $2 a barrel for the apples, and $3 a box for the oranges. How many of each did I buy?
Printed answer:- 3 bbls.; 9 boxes.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{b: 3, o: 9}
Exercise 5, problem 17
Divide the number 288 into three parts, so that the third part shall be twice the second, and the second five times the first.
Printed answer:- 18; 90; 180.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{f: 18, s: 90, t: 180}
Exercise 5, problem 18
Find two numbers whose sum is 216 and whose difference is 48.
Printed answer:- 84; 132.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 132, y: 84}
Exercise 5, problem 2
Twice a certain number added to five times the double of that number gives for the sum 36. What is the number?
Printed answer:- 3.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation3
On the STU-32 (STU, rpn):
2 ENTER 5 ENTER 2 × +
36 x↔y ÷
Calculator:
+3E+0; the book prints3. Run on the calculator core at firmware628c96c.Exercise 5, problem 3
Mr. James Cobb walked a certain length of time at the rate of 4 miles an hour, and then rode four times as long at the rate of 10 miles an hour, to finish a journey of 88 miles. How long did he walk and how long did he ride?
Printed answer:- Walked 2 hrs.; rode 8 hrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{w: 2, r: 8}
Exercise 5, problem 4
A man bought 3 books and 2 lamps for $14. The price of a lamp was twice that of a book. What was the cost of each?
Printed answer:- Book, $2; lamp, $4.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{b: 2, l: 4}
Exercise 5, problem 5
George bought an equal number of apples, oranges, and bananas for $1.08; each apple cost 2 cents, each orange 4 cents, and each banana 3 cents. How many of each did he buy?
Printed answer:- 12.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation12
On the STU-32 (STU, rpn):
108 ENTER 2 ENTER 4 + 3 +
÷
Calculator:
+12E+0; the book prints12. Run on the calculator core at firmware628c96c.Exercise 5, problem 6
I bought some 2-cent stamps and twice as many 5-cent stamps, paying for the whole $1.44. How many stamps of each kind did I buy?
Printed answer:- 12 twos; 24 fives.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{s: 12, f: 24}
Exercise 5, problem 7
I bought 2 pounds of coffee and 1 pound of tea for $1.31; the price of a pound of tea was equal to that of 2 pounds of coffee and 3 cents more. What was the cost of each per pound?
Printed answer:- Tea, 67; coffee, 32.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{c: 32, t: 67}
Exercise 5, problem 8
A lady bought 2 pounds of crackers and 3 pounds of gingersnaps for $1.11. If a pound of gingersnaps cost 7 cents more than a pound of crackers, what was the price of each?
Printed answer:- Crackers,18 gingersnaps, 25
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{k: 18, g: 25}
Exercise 5, problem 9
A man bought 3 lamps and 2 vases for $6. If a vase cost 50 cents less than 2 lamps, what was the price of each?
Printed answer:- Lamp, $1; vase, $1.50.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{l: 1, v: Rational(3, 2)}
Exercise 6
Exercise 6, problem 1
What number, being increased by 36, will be equal to ten times itself?
Printed answer:- 4.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation4
On the STU-32 (STU, rpn):
36 ENTER 10 ENTER 1 − ÷
Calculator:
+4E+0; the book prints4. Run on the calculator core at firmware628c96c.Exercise 6, problem 10
James is 3 years older than William, and twice James’s age is equal to three times William’s age. What is the age of each?
Printed answer:- W, 6 yrs.; J, 9 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{W: 6, J: 9}
Exercise 6, problem 11
One boy has 10 more marbles than another boy. Three times the first boy’s marbles equals five times the second boy’s marbles. How many has each?
Printed answer:- 25; 15 marbles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 25, b: 15}
Exercise 6, problem 12
If I add 12 to a certain number, four times this second number will equal seven times the original number. What is the original number?
Printed answer:- 16.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation16
On the STU-32 (STU, rpn):
12 ENTER 4 ×
7 ENTER 4 − ÷
Calculator:
+16E+0; the book prints16. Run on the calculator core at firmware628c96c.Exercise 6, problem 13
Four dozen oranges cost as much as 7 dozen apples, and a dozen oranges cost 15 cents more than a dozen apples. What is the price of each?
Printed answer:- Oranges, 35 cents; apples, 20 cents.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{o: 35, a: 20}
Exercise 6, problem 14
Two numbers differ by 6, and three times one number equals five times the other number. What are the numbers?
Printed answer:- 9; 15.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 15, y: 9}
Exercise 6, problem 15
A man is 2 years older than his wife, and 15 times his age equals 16 times her age. What is the age of each?
Printed answer:- 30 yrs.; 32 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{M: 32, W: 30}
Exercise 6, problem 16
A farmer pays just as much for 4 horses as he does for 6 cows. If a cow costs 15 dollars less than a horse, what is the cost of each?
Printed answer:- Cow, $30; horse,$45.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{h: 45, c: 30}
Exercise 6, problem 17
What number is that which is 15 less than four times the number itself?
Printed answer:- 5.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation5
On the STU-32 (STU, rpn):
15 ENTER 4 ENTER 1 − ÷
Calculator:
+5E+0; the book prints5. Run on the calculator core at firmware628c96c.Exercise 6, problem 18
A man bought 12 pairs of boots and 6 suits of clothes for $168. If a suit of clothes cost $2 less than four times as much as a pair of boots, what was the price of each?
Printed answer:- Boots, $5; clothes, $18.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{b: 5, s: 18}
Exercise 6, problem 2
Find the number whose double increased by 28 will equal six times the number itself.
Printed answer:- 7.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation7
On the STU-32 (STU, rpn):
28 ENTER 6 ENTER 2 −
÷
Calculator:
+7E+0; the book prints7. Run on the calculator core at firmware628c96c.Exercise 6, problem 3
If John’s age be multiplied by 5, and if 24 be added to the product, the sum will be seven times his age. What is his age?
Printed answer:- 12 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation12
On the STU-32 (STU, rpn):
24 ENTER 7 ENTER 5 − ÷
Calculator:
+12E+0; the book prints12. Run on the calculator core at firmware628c96c.Exercise 6, problem 4
A father gave his son four times as many dollars as he then had, and his mother gave him $25, when he found that he had nine times as many dollars as at first. How many dollars had he at first?
Printed answer:- $6.25.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equationRational(25, 4)
On the STU-32 (STU, rpn):
25 ENTER 4 ÷
Calculator:
+625E-2; the book prints25/4. Run on the calculator core at firmware628c96c.Exercise 6, problem 5
A man had a certain amount of money; he earned three times as much the next week and found $32. If he then had eight times as much as at first, how much had he at first?
Printed answer:- $8.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation8
On the STU-32 (STU, rpn):
32 ENTER 8 ENTER 4 −
÷
Calculator:
+8E+0; the book prints8. Run on the calculator core at firmware628c96c.Exercise 6, problem 6
A man, being asked how many sheep he had, said, "If you will give me 24 more than six times what I have now, I shall have ten times my present number." How many had he?
Printed answer:- 8 sheep.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation8
On the STU-32 (STU, rpn):
24 ENTER 10 ENTER 1 ENTER 6 + − ÷
Calculator:
+8E+0; the book prints8. Run on the calculator core at firmware628c96c.Exercise 6, problem 7
Divide the number 726 into two parts such that one shall be five times the other.
Printed answer:- 121; 605.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 121, y: 605}
Exercise 6, problem 8
Find two numbers differing by 852, one of which is seven times the other.
Printed answer:- 142; 994.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 142, y: 994}
Exercise 6, problem 9
A storekeeper received a certain amount the first month; the second month he received $50 less than three times as much, and the third month twice as much as the second month. In the three months he received $4850. What did he receive each month?
Printed answer:- $500; $1450; $2900.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 500, b: 1450, c: 2900}
Exercise 7
Exercise 7, problem 1
Roger is one-fourth as old as his father, and the sum of their ages is 70 years. How old is each?
Printed answer:- 14 yrs.; 56 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes{r: 14, f: 56}
Exercise 7, problem 10
Henry gave a third of his marbles to one boy, and a fourth to another boy. He finds that he gave to the boys in all 14 marbles. How many had he at first?
Printed answer:- 24 marbles.
verified: the printed answer passed a computed check
How it was checked
solve: passes24
On the STU-32 (STU, rpn):
14 ENTER 3 1/x 4 1/x + ÷
Calculator:
+2400000000000000000000000000000000E-32; the book prints24. Run on the calculator core at firmware628c96c.Exercise 7, problem 11
Two men own a third and two-fifths of a mill respectively. If their part of the property is worth $22,000, what is the value of the mill?
Printed answer:- $30,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes30000
On the STU-32 (STU, rpn):
22000 ENTER 3 1/x
2 ENTER 5 ÷ +
÷
Calculator:
+3000000000000000000000000000000000E-29; the book prints30000. Run on the calculator core at firmware628c96c.Exercise 7, problem 12
A fruit-seller sold one-fourth of his oranges in the forenoon, and three-fifths of them in the afternoon. If he sold in all 255 oranges, how many had he at the start?
Printed answer:- 300 oranges.
verified: the printed answer passed a computed check
How it was checked
solve: passes300
On the STU-32 (STU, rpn):
255 ENTER 1 ENTER 4 ÷
3 ENTER 5 ÷ +
÷
Calculator:
+3E+2; the book prints300. Run on the calculator core at firmware628c96c.Exercise 7, problem 13
The half, third, and fifth of a number are together equal to 93. Find the number.
Printed answer:- 90.
verified: the printed answer passed a computed check
How it was checked
solve: passes90
On the STU-32 (STU, rpn):
93 ENTER 2 1/x 3 1/x + 5 1/x +
÷
Calculator:
+9000000000000000000000000000000003E-32; the book prints90. Run on the calculator core at firmware628c96c.Exercise 7, problem 14
Mr. A bought one-fourth of an estate, Mr. B one-half, and Mr. C one-sixth. If they together bought 55,000 feet, how large was the estate?
Printed answer:- 60,000ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes60000
On the STU-32 (STU, rpn):
4 1/x 2 1/x +
6 1/x +
55000 x↔y ÷
Calculator:
+6000000000000000000000000000000000E-29; the book prints60000. Run on the calculator core at firmware628c96c.Exercise 7, problem 15
The wind broke off two-sevenths of a pine tree, and afterwards two-fifths more. If the parts broken off measured 48 feet, how high was the tree at first?
Printed answer:- 70ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes70
On the STU-32 (STU, rpn):
48 ENTER 2 ENTER 7 ÷ 2 ENTER 5 ÷ +
÷
Calculator:
+7000000000000000000000000000000000E-32; the book prints70. Run on the calculator core at firmware628c96c.Exercise 7, problem 16
A man spaded up three-eighths of his garden, and his son spaded two-ninths of it. In all they spaded 43 square rods. How large was the garden?
Printed answer:- 72 sq. rds.
verified: the printed answer passed a computed check
How it was checked
solve: passes72
On the STU-32 (STU, rpn):
3 ENTER 8 ÷ 2 ENTER 9 ÷ +
43 x↔y ÷
Calculator:
+7200000000000000000000000000000000E-32; the book prints72. Run on the calculator core at firmware628c96c.Exercise 7, problem 17
Mr. A’s investment in business is $15,000 more than Mr. B’s. If Mr. A invests three times as much as Mr. B, how much is each man’s investment?
Printed answer:- A, $22,500; B, $7500.
verified: the printed answer passed a computed check
How it was checked
solve: passes{A: 22500, B: 7500}
Exercise 7, problem 18
A man drew out of the bank $27, in half-dollars, quarters, dimes, and nickels, of each the same number. What was the number?
Printed answer:- 30.
verified: the printed answer passed a computed check
How it was checked
solve: passes30
On the STU-32 (STU, rpn):
27 ENTER 100 ×
50 ENTER 25 + 10 + 5 +
÷
Calculator:
+30E+0; the book prints30. Run on the calculator core at firmware628c96c.Exercise 7, problem 2
In a mixture of 360 bushels of grain, there is one-fifth as much corn as wheat. How many bushels of each?
Printed answer:- Corn, 60; wheat, 300.
verified: the printed answer passed a computed check
How it was checked
solve: passes{c: 60, w: 300}
Exercise 7, problem 3
A man bought a farm and buildings for $12,000. The buildings were valued at one-third as much as the farm. What was the value of each?
Printed answer:- $3000; $9000.
verified: the printed answer passed a computed check
How it was checked
solve: passes{b: 3000, f: 9000}
Exercise 7, problem 4
A bicyclist rode 105 miles in a day. If he rode one-half as far in the afternoon as in the forenoon, how far did he ride in each part of the day?
Printed answer:- 70 miles; 35 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes{a: 70, p: 35}
Exercise 7, problem 5
Two numbers differ by 675, and one is one-sixteenth of the other. What are the numbers?
Printed answer:- 45; 720.
verified: the printed answer passed a computed check
How it was checked
solve: passes{L: 720, s: 45}
Exercise 7, problem 6
What number is that which being diminished by one-seventh of itself will equal 162?
Printed answer:- 189.
verified: the printed answer passed a computed check
How it was checked
solve: passes189
On the STU-32 (STU, rpn):
162 ENTER 1 ENTER 7 1/x −
÷
Calculator:
+1890000000000000000000000000000000E-31; the book prints189. Run on the calculator core at firmware628c96c.Exercise 7, problem 7
Jane is one-fifth as old as Mary, and the difference of their ages is 12 years. How old is each?
Printed answer:- J, 3 yrs.; M, 15 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes{J: 3, M: 15}
Exercise 7, problem 8
The fourth and eighth of a number are together equal to 36. What is the number?
Printed answer:- 96.
verified: the printed answer passed a computed check
How it was checked
solve: passes96
On the STU-32 (STU, rpn):
36 ENTER 4 1/x ENTER 8 1/x +
÷
Calculator:
+96E+0; the book prints96. Run on the calculator core at firmware628c96c.Exercise 7, problem 9
A man left half his estate to his widow, and a fifth to his daughter. If they both together received $28,000, what was the value of his estate?
Printed answer:- $40,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes40000
On the STU-32 (STU, rpn):
28000 ENTER 2 1/x 5 1/x +
÷
Calculator:
+4000E+1; the book prints40000. Run on the calculator core at firmware628c96c.Exercise 7, problem None
*Illustrative Example*. Divide the number 72 into two parts such that one part shall be one-eighth of the other.
Printed answer:- (none printed)
verified: the printed answer passed a computed check
How it was checked
solve: passes64solve: passes100
On the STU-32 (STU, rpn):
72 ENTER 1 ENTER 8 1/x + ÷
Calculator:
+64E+0; the book prints64. Run on the calculator core at firmware628c96c.On the STU-32 (STU, rpn):
2 1/x 4 1/x +
75 x↔y ÷
Calculator:
+1E+2; the book prints100. Run on the calculator core at firmware628c96c.
Exercise 8
Exercise 8, problem 1
Three times a certain number increased by one-half of the number is equal to 14. What is the number?
Printed answer:- 4.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 4}
On the STU-32 (STU, rpn):
14 ENTER 3 ENTER 1 ENTER 2 ÷ + ÷
Calculator:
+4E+0; the book prints4. Run on the calculator core at firmware628c96c.Exercise 8, problem 10
A man, owning a lot of land, bought 3 other lots adjoining, -- one three-eighths, another one-third as large as his lot, and the third containing 14,000 feet, -- when he found that he had just twice as much land as at first. How large was his original lot?
Printed answer:- 48,000 ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 48000}
On the STU-32 (STU, rpn):
1 ENTER 3 ENTER 8 ÷ −
1 ENTER 3 ÷ −
1/x 14000 ×
Calculator:
+4799999999999999999999999999999999E-29; the book prints48000. Run on the calculator core at firmware628c96c.Exercise 8, problem 11
What number is doubled by adding to it two-fifths of itself, one-third of itself, and 8?
Printed answer:- 30.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 30}
On the STU-32 (STU, rpn):
2 ENTER 5 ÷ 1 ENTER 3 ÷ + 1 + 2 −
8 +/− x↔y ÷
Calculator:
+2999999999999999999999999999999996E-32; the book prints30. Run on the calculator core at firmware628c96c.Exercise 8, problem 12
There are three numbers whose sum is 90; the second is equal to one-half of the first, and the third is equal to the second plus three times the first. What are the numbers?
Printed answer:- 18; 9; 63.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 18, y: 9, z: 63}
Exercise 8, problem 13
Divide 84 into three parts, so that the third part shall be one-third of the second, and the first part equal to twice the third plus twice the second part.
Printed answer:- 56; 21; 7.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 56, y: 21, z: 7}
Exercise 8, problem 14
Divide 112 into four parts, so that the second part shall be one-fourth of the first, the third part equal to twice the second plus three times the first, and the fourth part equal to the second plus twice the first part.
Printed answer:- 16; 4; 56; 36.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 16, y: 4, z: 56, w: 36}
Exercise 8, problem 15
A grocer sold 62 pounds of tea, coffee, and cocoa. Of tea he sold 2 pounds more than of coffee, and of cocoa 4 pounds more than of tea. How many pounds of each did he sell?
Printed answer:- Coffee, 18 lbs.; tea, 20 lbs.; cocoa, 24 lbs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{c: 18, t: 20, k: 24}
Exercise 8, problem 16
Three houses are together worth six times as much as the first house, the second is worth twice as much as the first, and the third is worth $7500. How much is each worth?
Printed answer:- $2500; $5000; $7500.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{a: 2500, b: 5000, c: 7500}
Exercise 8, problem 17
John has one-ninth as much money as Peter, but if his father should give him 72 cents, he would have just the same as Peter. How much money has each boy?
Printed answer:- J, 9 cents; P, 81 cents.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{j: 9, p: 81}
Exercise 8, problem 18
Mr. James lost two-fifteenths of his property in speculation, and three-eighths by fire. If his loss was $6100, what was his property worth?
Printed answer:- $12,000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 12000}
On the STU-32 (STU, rpn):
6100 ENTER 2 ENTER 15 ÷
3 ENTER 8 ÷ +
÷
Calculator:
+1200000000000000000000000000000000E-29; the book prints12000. Run on the calculator core at firmware628c96c.Exercise 8, problem 2
Three boys have an equal number of marbles. John buys two-thirds of Henry’s and two-fifths of Robert’s marbles, and finds that he then has 93 marbles. How many had he at first?
Printed answer:- 45 marbles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{m: 45}
On the STU-32 (STU, rpn):
2 ENTER 3 ÷
1 +
2 ENTER 5 ÷ +
93 x↔y ÷
Calculator:
+4499999999999999999999999999999999E-32; the book prints45. Run on the calculator core at firmware628c96c.Exercise 8, problem 3
In three pastures there are 42 cows. In the second there are twice as many as in the first, and in the third there are one-half as many as in the first. How many cows are there in each pasture?
Printed answer:- 12; 24; 6 cows.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 12, y: 24, z: 6}
Exercise 8, problem 4
What number is that which being increased by one-half and one-fourth of itself, and 5 more, equals 33?
Printed answer:- 16.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 16}
On the STU-32 (STU, rpn):
1 ENTER 2 1/x +
4 1/x +
33 ENTER 5 −
x↔y ÷
Calculator:
+16E+0; the book prints16. Run on the calculator core at firmware628c96c.Exercise 8, problem 5
One-third and two-fifths of a number, and 11, make 44. What is the number?
Printed answer:- 45.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 45}
On the STU-32 (STU, rpn):
44 ENTER 11 −
ENTER 3 ENTER 5 × ×
5 ENTER 2 ENTER 3 × + ÷
Calculator:
+45E+0; the book prints45. Run on the calculator core at firmware628c96c.Exercise 8, problem 6
What number increased by three-sevenths of itself will amount to 8640?
Printed answer:- 6048.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 6048}
On the STU-32 (STU, rpn):
8640 ENTER 7 ×
7 ENTER 3 + ÷
Calculator:
+6048E+0; the book prints6048. Run on the calculator core at firmware628c96c.Exercise 8, problem 7
A man invested a certain amount in business. His gain the first year was three-tenths of his capital, the second year five-sixths of his original capital, and the third year $3600. At the end of the third year he was worth $10,000. What was his original investment?
Printed answer:- $3000.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 3000}
On the STU-32 (STU, rpn):
10000 ENTER 3600 −
1 ENTER 3 ENTER 10 ÷ +
5 ENTER 6 ÷ +
÷
Calculator:
+3000000000000000000000000000000000E-30; the book prints3000. Run on the calculator core at firmware628c96c.Exercise 8, problem 8
Find the number which, being increased by its third, its fourth, and 34, will equal three times the number itself.
Printed answer:- 24.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 24}
On the STU-32 (STU, rpn):
34 ENTER 3 ENTER 1 −
1 ENTER 3 ÷ −
1 ENTER 4 ÷ −
÷
Calculator:
+2399999999999999999999999999999999E-32; the book prints24. Run on the calculator core at firmware628c96c.Exercise 8, problem 9
One-half of a number, two-sevenths of the number, and 31, added to the number itself, will equal four times the number. What is the number?
Printed answer:- 14.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{x: 14}
On the STU-32 (STU, rpn):
31 ENTER 4 ENTER 1 ENTER 2 ÷ −
2 ENTER 7 ÷ −
1 −
÷
Calculator:
+1400000000000000000000000000000000E-32; the book prints14. Run on the calculator core at firmware628c96c.
Exercise 9
Exercise 9, problem 1
Divide the number 56 into two parts, such that one part is three-fifths of the other.
Printed answer:- 35; 21.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"x": 35, "y": 21}
Exercise 9, problem 10
A man bought a lot of lemons for $5; for one-third he paid 4 cents apiece, and for the rest 3 cents apiece. How many lemons did he buy?
Printed answer:- 150 lemons.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation150
On the STU-32 (STU, rpn):
4 ENTER 3 ÷ 2 +
5 ENTER 100 × x↔y ÷
Calculator:
+1500000000000000000000000000000000E-31; the book prints150. Run on the calculator core at firmware628c96c.Exercise 9, problem 11
A lot of land contains 15,000 feet more than the adjacent lot, and twice the first lot is equal to seven times the second. How large is each lot?
Printed answer:- 21,000 ft.; 6000 ft.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"A": 21000, "B": 6000}
Exercise 9, problem 12
A bicyclist, in going a journey of 52 miles, goes a certain distance the first hour, three-fifths as far the second hour, one-half as far the third hour, and 10 miles the fourth hour, thus finishing the journey. How far did he travel each hour?
Printed answer:- 20; 12; 10; l0 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"a": 20, "b": 12, "c": 10, "d": 10}
Exercise 9, problem 13
One man carried off three-sevenths of a pile of loam, another man four-ninths of the pile. In all they took 110 cubic yards of earth. How large was the pile at first?
Printed answer:- 126 cu. yds.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation126
On the STU-32 (STU, rpn):
110 ENTER 3 ENTER 7 ÷ 4 ENTER 9 ÷ + ÷
Calculator:
+1260000000000000000000000000000000E-31; the book prints126. Run on the calculator core at firmware628c96c.Exercise 9, problem 14
Matthew had three times as many stamps as Herman, but after he had lost 70, and Herman had bought 90, they put what they had together, and found that they had 540. How many had each at first?
Printed answer:- M, 390; H, 130.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"H": 130, "M": 390}
Exercise 9, problem 15
It is required to divide the number 139 into four parts, such that the first may be 2 less than the second, 7 more than the third, and 12 greater than the fourth.
Printed answer:- 39; 41; 32; 27.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"p1": 39, "p2": 41, "p3": 32, "p4": 27}
Exercise 9, problem 16
In an election 7105 votes were cast for three candidates. One candidate received 614 votes less, and the other 1896 votes less, than the winning candidate. How many votes did each receive?
Printed answer:- 3205; 2591; 1309.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"S": 2591, "T": 1309, "W": 3205}
Exercise 9, problem 17
There are four towns, A, B, C, and D, in a straight line. The distance from B to C is one-fifth of the distance from A to B, and the distance from C to D is equal to twice the distance from A to C. The whole distance from A to D is 72 miles. Required the distance from A to B, B to C, and C to D.
Printed answer:- 20 miles; 4 miles; 48 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"AB": 20, "BC": 4, "CD": 48}
Exercise 9, problem 2
If the sum of two numbers is 42, and one is three-fourths of the other, what are the numbers?
Printed answer:- 24; 18.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"a": 18, "b": 24}
Exercise 9, problem 3
The village of C---- is situated directly between two cities 72 miles apart, in such a way that it is five-sevenths as far from one city as from the other. How far is it from each city?
Printed answer:- 42; 30 miles.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"x": 30, "y": 42}
Exercise 9, problem 4
A son is five-ninths as old as his father. If the sum of their ages is 84 years, how old is each?
Printed answer:- 30; 54 yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"f": 54, "s": 30}
Exercise 9, problem 5
Two boys picked 26 boxes of strawberries. If John picked five-eighths as many as Henry, how many boxes did each pick?
Printed answer:- J, 10 boxes; H, 16 boxes.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"H": 16, "J": 10}
Exercise 9, problem 6
A man received 60-1/2 tons of coal in two carloads, one load being five-sixths as large as the other. How many tons in each carload?
Printed answer:- 33 tons; $27\frac{1}{2}$ tons.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"a": "55/2", "b": 33}
Exercise 9, problem 7
John is seven-eighths as old as James, and the sum of their ages is 60 years. How old is each?
Printed answer:- John, 28yrs.; James, 32yrs.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"J": 28, "M": 32}
Exercise 9, problem 8
Two men invest $1625 in business, one putting in five-eighths as much as the other. How much did each invest?
Printed answer:- $1000; $625.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"a": 625, "b": 1000}
Exercise 9, problem 9
In a school containing 420 pupils, there are three-fourths as many boys as girls. How many are there of each?
Printed answer:- 240 girls; 180 boys.
verified: the printed answer passed a computed check
How it was checked
solve: passes, with the problem read into an equation{"b": 180, "g": 240}