RULE.

Put the quantity which is of the same kind as the answer for the third term.

Place the greater of the other two numbers in the second term when the result is to be greater, and in the first term when the result is to be less, than the third term, and the remaining number in the unoccupied term.

Divide the product of the means by the given extreme.

3. If 15 cords of wood cost $112.50, what will 34 cords cost?

4. If 12 men can do a piece of work in 53 days, how long will it require 22 men to do it?

5. What will 75 acres of land cost, if 22 acres cost $3520? 6. If 42 bushels of potatoes cost $25, what will 52 bushels cost?

7. If 40 men can do a piece of work in 289 days, in what time can 17 men do it?

8. If 3

tons of coal cost $18, what will 14 tons cost?

9. If 7 tons of coal can be bought for $467, how many tons can be bought for $150?

10. If 8 horses consume 14 tons of hay in a certain time, how much will 51 horses consume in the same time?

11. If 16 horses consume a quantity of oats in 142 days, how long will it last 40 horses?

12. If a pole 57 feet high casts a shadow 42 ft. long, how long will be the shadow of a pole 114 ft. high?

13. A failed in business, and can pay only 62 cents on each dollar of his indebtedness; how much will B receive, whose claim against A is $825.75?

14. If 250 men can do a piece of work in 163 days, how long will it require 42 men to do it?

15. If 12 tons of hay cost $180.25, what will 81 tons cost?

16. A regiment of 960 men has provision for 40 days; how long will it last if the regiment is reinforced by 240 men?

17. A walked 156 rods in 13 minutes; how long will it take him to walk a mile?

18. If 96 men can dig a ditch in 413 days, how long will it require 57 men to dig it?

19. A garrison of 560 men has provision for 240 days: a reinforcement is received, and the provision lasts but 80 days; how many men in the reinforcement?

20. If 125 acres of land cost $10500, what will 17 acres cost at $4 less an acre?

21. If 42 men can do a piece of work in 64 days, how long will it take to do one-half of it if 12 men refuse to work?

22. If 54 men can do a piece of work in 96 days, how long will it take to complete the work if 8 men leave when it is onethird done?

23. If it requires 145 days to complete a piece of work by working 10 hours a day, how long will it take by working 71⁄2 hours a day?

24. If a field 60 rods long and 20 rods wide cost $500, what will a field 15 chains long and 8 chains wide cost?

25. A family of 10 persons have provision for 212 days: at the end of 42 days 2 persons leave; how long will the remainder of the provision last ?

26. A's rate of working is to B's as 4:7; how long will it take A to do what B does in 63 days?

27. If 5 bu. 3 pk. of potatoes cost $4.60, what will 2 bu. 1 pk. cost at the same rate?

28. If a lot of ground 50 feet wide by 126 feet deep contains 700 square yards, how deep must a lot be that is 75 feet wide to contain the same area?

29. My watch gains 3 min. 10 sec. a day; if it is set right on Monday morning at 6 A. M., what is the time by my watch on the following Saturday afternoon at 4 P. M., correct time?

205. Compound Proportion.

A Compound Proportion is a proportion in which one or both ratios are compound (ART. 201); as,

PROBLEMS IN COMPOUND PROPORTION.

1. If 8 men build 240 feet of wall in 60 days of 10 hours each, how many feet of wall will 12 men build in 80 days of 8 hours each?

Since the answer is to be feet, we make 240 feet the third term.

If 8 men build 240 feet of wall, 12 men will build more wall, other things being equal; hence the answer would be greater than the third term, and the first ratio is 8: 12.

Again, if 240 feet of wall are built in 60 days, in 80 days more wall can be built, other things being equal; hence the answer would be greater than the third term, and the second ratio is 60: 80.

Also, if 240 feet of wall are built by working 10 hours a day, a less number of feet of wall will be built by working 8 hours a day, other things being equal; hence the answer would be less than the third term, and the third ratio is 10: 8.

The work therefore stands as follows:

2. If 40 men earn $1280 in 16 days, how much will 36 men earn in 31 days?

3. If 12 men dig a trench 40 rods long in 24 days of 10 hours each, how many rods can 16 men dig in 18 days of 9 hours each?

4. If 42 men can build a wall 56 rods long in 96 days, how many men will be required to build 63 rods in 84 days?

5. If $500 in 4 yr. at 6% gain $120 interest, how much will $560 gain in 10 yr. at 5% ?

6. If a man travel 360 miles in 15 days of 7 hours each, how far will he travel in 14 days of 10 hours each?

7. If a man travel 540 miles in 20 days of 10 hours each, how many hours a day must he travel to cover 630 miles in 25 days?

8. If 10 planks 18 ft. long, 16 in. wide, 2 in. thick cost $12, what cost 25 planks 16 ft. long, 15 in. wide, and 3 in. thick?

9. If 30 men, working 10 hours a day, dig in 20 days a trench 400 rods long, 4 ft. wide, and 5 feet deep, in how many days can 36 men, working 8 hours a day, dig a trench 240 rods long, 5 feet wide, and 6 feet deep?

10. If a piece of iron 7 feet long, 4 inches wide, and 6 inches thick weighs 600 pounds, how much will a piece of iron weigh that is 16 feet long, 8 inches wide, and 4 inches thick?

11. If 10 men can build 120 rods of fence in 12 days of 93 hours each, how many hours a day will 16 men have to work to build 300 rods of fence in 25 days?

12. If 24 men can build a wall 72 rods long, 6 feet wide, and 5 feet high in 60 days of 10 hours each, how many days will it take 32 men to build a wall 96 rods long, 4 feet wide, and 8 feet high, working 8 hours a day?

13. If from 40 cows, each giving 12 quarts of milk daily, 15 cheeses of 40 pounds each are made in 15 weeks, how many cows will produce 25 cheeses of 60 pounds each in 12 weeks, if they give 10 quarts each daily?

14. If 12 compositors in 30 days of 10 hours each set up 25 sheets of 16 pages each, 32 lines on a page, in how many days 8 hours long can 18 compositors set up, in the same type, 64 sheets of 12 pages each, 40 lines on a page?

PARTNERSHIP.

206. A Partnership is an association formed by two or more persons for the transaction of business.

The Partners are the persons forming the partnership.

The Capital is the money invested.

The Assets or Resources of a partnership are its property of any kind.

The Liabilities are its debts.

207. Simple Partnership.

In Simple Partnership each partner's capital is invested for the same time, and the profits or losses are divided in proportion to their capital.

WRITTEN EXERCISES.

1. A, B, and C form a partnership: A puts in $5000, B $4000, and C $3000; if they gain $3840, what is each one's share of the gain?

The capital invested is $5000 + $4000 + $3000, or $12000. If $12000 gain $3840, $1 will gain $.32. Then,

2. A and B formed a partnership: A put in $4200 and B $3400; they gained $1824; what was each man's share of the gain?

3. A, B, and C engaged in business with a capital of $13000: A put in $5100, B $4800, and C the remainder; they gained $5200; what was each one's share of the gain?

4. Four men engaged in business: L put in $5000, M $6000, N $7000, and O $8000; they lost $3380; what was each one's share of the loss?