RULE OF THREE BY ANALYSIS.

195. The solution of questions in the Rule of Three by analysis consists in finding the ratio of two of the given terms, and multiplying this ratio by the other term.

The ratio of two of the terms will generally express the value or cost of a single thing.

EXAMPLES.

1. If 3 barrels of flour cost $24, what will 7 barrels cost? By dividing the $24 by 3 we get the cost of 1 barrel. For, if $24 will buy 3 barrels, it is plain that of it will buy 1 barrel. This, multiplied by 7, gives $56 the cost of 7 barrels.

OPERATION

3)24 8

8 × 7 = 56

Ans. $56.

2. If in 20 days a man travels 58 miles, how far will he travel in 30 days?

3. If 6 men consume 1 barrel of flour in 30 days, how much would 48 men consume?

It is evident that of a barrel would be the amount consumed by 1 man: hence, 48 times is the amount consumed by 48

men.

OPERATION.

1/2 × 48 8. Ans. 8.

4. If 2 barrels of flour cost $13, what will 12 barrels cost? 5. If I walk 168 miles in 6 days, how far should I walk at the same rate in 18?

6.`If 8lb. of sugar cost $1,28, how much will 137b. cost? What is 16 × 13 ?

7. If of a piece of cloth cost $8,25, what will 2 cost? 8. If 300 barrels of flour cost $570, what will 200 cost? What is × 570 ?

9. If of a barrel of cider cost of a dollar, what will g cost? What is 21 What is 21 × 11?

40

9

QUEST.-195. In what does the solution of questions by analysis consist? What does the ratio of the two terms express? If this ratio be multiplied by the other term, what will be the product?

10 If 90 bushels of oats will feed 40 horses for 6 days, how long would 450 bushels feed them?

11. If 5 oxen, or 7 colts, eat up a certain quantity of grass. in 87 days, in what time will 2 oxen and 3 colts eat up the same quantity of grass?

12. A person's income is £146 per annum: how much is that each day?

13. If 3 paces of common steps be equal to 2 yards, how many yards will 160 paces make?

14. A certain work can be done in 12 days by working 4 hours each day: how long would it require to do the work by working 9 hours a day?

15. A pasture of a certain extent having supplied a body of horse, consisting of 3000, with forage for 18 days, how many days would the same pasture have supplied a body of 2000 horse?

16. The governor of a besieged city has provisions for 54 days, at the rate of 2lb. of bread per day, but is desirous of prolonging the siege to 80 days, in expectation of succor in that case what must be the allowance of bread per day?

17. If a person pays half a guinea a week for his board, how long can he be boarded for £21?

18. If a person drinks 80 bottles of wine per month, when it costs 2s. per bottle, how much can he drink, without increasing the expense, when it costs 2s. 6d. per bottle?

19. How long will a person be in saving £100, if he saves 1s. 6d. per week?

20. A merchant bought 21 pieces of cloth, each containing 41 yards, for which he paid $1260; he sold the cloth at $1,75 per yard: did he gain or lose by the bargain?

21. A grocer bought a puncheon of rum for £41 14s. 6d., to which he added as much water as reduced its cost to 5s. 6d. per gallon; how much water did he put in?

22. If one pound of tea be equal in value to 50 oranges, and 70 oranges be worth 84 lemons, what is the value of a pound of tea when a lemon is worth two cents?

RULE OF THREE BY CANCELLING.

196. The cancelling process may be applied to all ques tions in the Rule of Three, where the second or third terms have a factor common to the first. Let the second and third terms be written above the line, with the sign of multiplication between them, and the first term below it, and then cancel the common factors.

EXAMPLES.

1. If 48 yards of cloth cost $67,25, what will 144 yards cost?

The process here is obvious, being entirely similar to that explained in Art. 191.

OPERATION.

3

67,25 ×
48

= $201,75.

2. If 25 yards of cloth cost £2 3s. 4d., what will 5 yards

cost?

3. If 24 hats cost $120, how much will 80 cost?

4. If 90 barrels of flour will subsist 100 men for 120 days, how long will it subsist 75 ?

5. If 60 sheep yield 180lb. of wool, how many pounds will be obtained from 900?

6. If a man travel 210 miles in 6 days, how far will he travel in 120 days?

7. If the freight of 40 tierces of sugar, each weighing 3 cwt., 150 miles, cost $42, what must be paid for the freight of 10 hogsheads, each weighing 12cwt., 50 miles?

8. A certain amount of provisions will subsist an army of 9000 men for 90 days: if the army be increased by 4500, how long would the same provisions subsist it?

9. If 50 persons consume 600 bushels of wheat in one year, how much will 278 persons consume in 7 years?

10. If 3 yards of cloth cost 18s., what will 24 yards cost?

QUEST.-196. To what questions may the cancelling process be applied? How are the numbers written? What factors do What factors do you cancel?

11. If 112 pounds of sugar cost 56s., what will 1 pound cost?

12. If 4 men can do a piece of work in 80 days, how many days of the same length will 16 men require to do the same work?

13. If 21 pioneers make a trench in 18 days, how many days of the same length will 7 men require to make a similar trench?

14. If a field of grass be mowed by 10 men in 12 days, in how many days would it be mowed by 20 men ?

15. A certain piece of grass was to be mowed by 20 men in 6 days; an extraordinary occasion calls off half the workmen. It is required to find in what time the rest will finish it.

16. If the penny loaf weighs 5oz. when flour is 2s. a peck, what should it weigh when flour is sold for 2s. 6d. a peck?

17. Provisions in a garrison are found sufficient to last 1800 soldiers for three months; but a reinforcement being wanted that the provisions may last for one month only, what number of soldiers must be added to the garrison?

18. If 3yd. 2qr. of cloth of lyd. 3qr. wide will make a suit of clothes, how many yards of stuff of 3qr. wide will make a suit for the same person?

19. If I lend my friend £200 for 12 months on condition of his returning the favor, how long ought he to lend me £150 to requite my kindness?

20. If an acre be 220 yards long, the breadth will be 22 yards; but if the breadth of an acre be 40 yards, what then will be the length?

21. How many pounds of sugar at 12d. per pound are equal in value to 24lb. of tea, worth 9s. 6d. per pound?

22. A tax of £225 10s. was laid upon four villages A, B, C, and D; it had been the custom with these villages, that whenever any taxes were to be levied, as often as A, B, and C paid each 3d., D paid only 2d.: how much did each village pay?

EXAMPLES INVOLVING FRACTIONS.

1. If 3 of a yard of cloth cost $3,20, what will 21 yards

vert the terms of the divisor and multiply.

2. If oz. cost £11, what will 1oz. cost?

16

Ans.

5

3. If of a ship cost £273 3s. 6d., what will 11⁄2 of her cost?

4. If 375 yards of cloth cost £164 9d. what will 257 yards cost?

5. If 14 yards of cloth can be bought for 10 guineas, how many ells Flemish can be bought for £283.875 ?

6. If 12oz. of plate cost 10s. 114d., what will a service weighing 327.61875oz. cost?

7. If 143lb. of sugar cost $13, what will 12lb. cost?

8. If of a yard of cloth cost $15, what will 71 yards cost?

9. If 2 men can do 125 rods of ditching in 65 days, in how many days can 18 men do 2424 rods?

10. If a wedge of gold weighing 173lb. troy, be worth £6795, what is the value of 1qr. of that gold?

11. If the carriage of 2.5 tons of goods 2.9 miles cost 0.75 guinea, what is that per cwt. for a mile?

12. If cwt. of tobacco cost £4 18s., how much may be bought for £7?