Examples.

2. If 12 bushels of wheat cost $16, what will 30 bushels cost? Ans. $40. 3. If the rent of a farm of 183 acres is $273, what will be the rent of a farm of 61 acres? Ans. $91. 4. If 98 bushels of potatoes cost $56, how many bushels can be had for $16? Ans. 28 bushels. 5. When 12 yards of cloth can be bought for $16, how many can be bought for $72? Ans. 54 yards. 6. A person completed a journey of 40 miles in five hours; how far, at the same rate, can he travel in 45 hours?

Ans. 360 miles.

7. If 5 yards of cloth cost $63, what will 12% yards cost? Ans. $15.81. 8. If 385 kilos of sugar cost $63, how many may be bought for $18?

9. If I can complete a piece of work in 32 days, by working 8 hours a day, in what time can I do the same by working only 6 hours a day? Ans. 42 days. 10. If I borrowed of a friend $300 for 8 months, for how long a time should I lend him $200 in return?

Ans. 12 months.

11. If 100 workmen can do a piece of work in 12 days, how many can do the same in 8 days?

12. How many yards of flannel 2 of a yard wide are required to line a cloak which has in it 12 yards of cloth of a yard wide? Ans. 8 yards. 13. If I give $2 for .4 of a cord of wood, how much must I give for of a cord?

Ans. $1.25.

14. If of a ship cost $9750, what will 1⁄2 of it cost?

Ans. $42000.

REVIEW QUESTIONS. What is Ratio? (320) Terms of a ratio? (321) A Simple Ratio? (323) A Compound Ratio? (324) Principles of ratio! 325)

15. Two numbers are to each other as 15 to 34, and the smaller is 75; what is the greater? Ans. 170.

16. Two numbers are to each other as 3 to 2, and the greater is 210; what is the smaller?

17. If 3 cords 5 cord feet of wood will purchase 1 T. 5 cwt. 3 qr. of hay, what quantity of wood will be required to purchase 1 ton of hay? Ans. 2 C. 6+ c. ft.

18. If a railway train moves 150 miles in 5 hours, in what time will it move 225 miles? Ans. 8 h. 15 m. 19. If 8 boarders consume a certain quantity of provisions in 10 days, how many days would it have lasted if 2 more had been in the company? Ans. 8 days.

20. A besieged fortress has provisions for 3 weeks, at the rate of 14 ounces a day for each man; at what rate per day must the provisions be distributed, so that the place may hold out 5 weeks? Ans. 8 oz.

21. If the fore wheel of a coach, which is 7 feet 6 inches in circumference, turns round 70400 times in going a hundred miles, how often will the hind wheel, which is 9 feet 2 inches, turn round in going the same distance? Ans. 57600 times. 22. If 125 bushels of wheat grow on 4 acres 84 square rods, how much land will be required to produce 650 bushels ? Ans. 23 A. 84.8 P.

23. If a stick 7 feet high cast a shadow 5 feet in length, what is the hight of a spire that casts a shadow 129 feet in length? Ans. 180 ft. 7 in.

24. A besieged town, containing 22400 inhabitants, has provisions to last 3 weeks; how many must be sent away that they may be able to hold out 7 weeks? Ans. 12800.

331. When it is required to divide a quantity into parts which are proportional to given numbers, we may.

Add together the proportional numbers; then, the sum of

REVIEW QUESTIONS. What is Proportion? (326) Terms of a Propor tion? (327) Principles ? (328)

these numbers will be to any one of them, as the quantity to be divided is to the part corresponding to that number.

25. A gentleman bequeathed $18000 to his three sons, A, B, and C, in the proportion of 3, 4, and 5; how much was the part of each?

Since the given sum is to be bequeathed to the three sons, in the proportion of 3, 4, and 5, if we divide $18000 into 3+4+5, or 12,

equal parts, A will have 3, B 4, and C 5, of these parts. Hence, A's part is of $18000, or $4500, B's of $18000, or $6000, and C's of $18000, or $7500.

26. Two men own a field of 640 acres in common, and their respective shares of it are in the ratio of 7 to 9; if divided, how many acres would belong to each ?

27. Divide 4720 into 3 parts which shall be in the proportion of,, and . Ans. 1200, 1600, and 1920. 28. In a certain town of 4500 inhabitants, the youth are to the adults in the ratio of 13 to 12; required the number of each. Ans. Youth, 2340; adults, 2160.

COMPOUND PROPORTION.

332. Compound Proportion is an equality between a compound and a simple ratio. Thus,

3:4

5 : 8

:: 45 96 is a compound proportion.

It applies to the solution of questions which would require several simple proportions.

333. To solve questions by compound proportion. 1. If 4 men can earn $96 in 8 days, how much can 10 men earn in 6 days?

How may we proceed when it is required to divide a quantity into parts which are proportional to given numbers? Explain the operation. What is Compound Proportion? To what does it apply?

4: 10
8: 6

OPERATION.

:: $96: amount required; or

4 X 8: 10 × 6: $96: amount required.

3

Then,

$96 X 10 X 6
4X8

= $180

= amount required.

If 4 men can earn $96 in 8 days, 1 man can earn in the same time of $96, or $24, and 10 men can earn 10 times $24, or $240. If 10 men can earn $240 in 8 days, in 1 day they can earn § of $240 or $30, and in 6 days 6 times $30, $180.

Or, if 4 men can earn $96 in 8 days, 10 men in the same time will earn 10 of $96, and in 6 days, § of 10 of $96, or $180.

RULE. Write the given number of the same kind as the answer for the third term; and arrange the remaining numbers, each pair of the same kind, as in simple proportion.

Find the required term by dividing the product of the third and second terms by the product of the first terms.

It is recommended to solve the questions by both compound proportion and analysis.

Examples.

2. If a pasture of 16 acres will feed 6 horses for 4 months, how will feed 12 horses for 9 months? Ans. 72 acres. many acres 3. If 36 yards of cloth, 7 quarters wide, be worth $98, what is the value of 120 yards of equal quality, but only 5 quarters wide?

4. If 6 men can mow 16 acres in 4 days, how long will it take 10 men to mow 40 acres, at the same rate? Ans. 6 days.

5. If a man travel 90 miles in 3 days, by walking 8 hours ? day, in what time will he travel 540 miles, by walking 6 hours a day? Ans. 24 days. 6. If a family of 9 spend $600 in 8 months, how much will serve a family of 24 for 16 months? Ans. $3200.

Explain the operation. Repeat the Rule.

7. If 12 horses in 5 days plow 11 acres, how many horses would plow 33 acres in 18 days? Ans. 10 horses. 8. If $2000 will support a garrison of 150 men 3 months, how long will $6000 support 4 times as many men?

9. The interest on $200 for 4 months being $4, what will be the interest on $590 for 1 year and 3 months? Ans. $44.25. 10. When 12 men can put of a cargo on board of a ship in of a day, how long would it require 5 men to load 3 such vessels? Ans. 13 days.

11. If $750 will defray the expenses of 12 men for 14 weeks 2 days, how much will 5 men require for 22 weeks 6 days?

Ans. $500.

12. If 18 men can dig a trench 30 yards long in 24 days, by working 8 hours a day, how many will dig a trench 60 yards long in 64 days, working 6 hours a day? Ans. 18 men. 13. If 29 men in 5 days of 12 hours each can reap 32 acres, how many acres can 20 men reap in 83 days of 13 hours each? Ans. 40 acres.

PARTNERSHIP.

334. Partnership is the association of two or more persons in business, under a certain name, with an agreement to share the profits and losses.

The PARTNERS are the individuals associated.

The COMPANY, or FIRM, is the business association.

The CAPITAL, or STOCK, is the money, or property used ir business.

A DIVIDEND is the profits to be divided.

The profits and losses of a firm are usually distributed among the partners in proportion to their respective shares in the business.

REVIEW QUESTIONS. A Simple Proportion? (329) The Rule? (330) What is Partnership? The Partners ? The Company or Firm? The Capital or Stock? A Dividend?