3. If 3 men or 6 women can do a piece of work in 56 days, in what time will 1 man and 2 women working together do it?

4. If 5 men can do as much in a day as 8 boys, how long will it take 32 boys to finish a piece of work which 15 men can do in 12 days?

5. If $100 gain $4 in 1 year, what will $350 gain in 31 years?

6. If 48 horses in 10 days consume 180 bu. oats, how many bushels will 32 horses consume in 10 days? In 12 days? In 15 days?

7. If 5 men mow 45 acres of grass in 6 days, in how many days will 12 men mow 90 acres?

974. In practice, the work is somewhat shortened. Since the number of days is required, we write the given number of days last, with a line underneath.

If 5 men do the work in a certain time, 1 man will require 5 times as many days. We place 5 in the numerator (as a multiplier). To cut 1 acre, he will take of the time required to cut 45 acres. Place 45 in the denominator (as a divisor).

12 men will take of the time 1 man requires. Place 12 in the denominator. To cut 90 acres will require 90 times as long. Place 90 in the numerator.

8. If 12 horses eat 60 bushels of oats in 6 days, how many bushels will 24 horses eat in 3 days?

975. This example can be solved more easily. 6 days' food for 12 horses will supply how many horses for 1 day? 3 days' food for 24 horses will supply how many horses for 1 day?

9. If 24 men use 240 lb. of beef in 2 weeks, how many pounds will 18 men use in 8 weeks?

24 men in 2 weeks use 240 lb.

10. If 6 printers can print 1,656 sheets in 9 days, how many sheets will 15 printers print in 10 days?

11. How much will it cost to feed 520 sheep for 36 days, if it costs $128 to feed 160 sheep 48 days?

12. In what time will 8 masons build a wall 84 ft. long, working 10 hours a day, if 12 masons build a wall 96 ft. long in 8 days, working 8 hours a day?

13. How much money must I lend for 1 year and 3 months, when the rate of interest is 5 per cent, in return for $60 lent me for 9 months, which I borrowed at 4 per cent?

14. If 27 men build 54 rods of wall in 6 days, how many rods will 32 men build in 9 days?

15. If 50 men can do a piece of work in 90 days, working 8 hours a day, in how many days will 72 men do it, working 10 hours a day?

16. If $350 earns $42 interest in 3 years, how much will $225 earn in 5 years?

17. If a wall 34 feet high could be built by 68 men in 15 days, how many men could build a wall 32 feet high in 8 days?

18. If a ship's crew of 500 men have provisions to serve for 48 days, at the rate of 27 ounces a day for each man, how many men will the same provisions serve for 60 days, allowing each man 30 ounces a day?

19. How many hours a day must 9 men work so that they may do as much in 16 days as 12 men can do in 15 days of 8 hours each?

20. If 30 is paid for 6 lb. 14 oz. of bread, when wheat is $1.14 per bu., what should be paid for 23 lb. 12 oz., when wheat is $1.32 per bu.?

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NOTE. Reduce weights to ounces, or to pounds and fractions.

21. If 3 men can do as much work as 7 boys, how long will it take 28 boys to do as much work as 16 men can do in 24 days?

22. A crew of 16 men have provisions for 36 days, allowing 20 ounces to each man per day. After sailing 10 days they pick up 10 shipwrecked sailors. How long will the provisions then last at the daily rate of 16 ounces per man?

PARTNERSHIP.

977. Slate Problems.

1. B and C gain by trade $182. What is the gain of each, B having put in $300, and C $400?

The gain of $700 is $182. What should $300 gain? What should $400 gain?

2. A, B, and C invest $720, $340, and $960, respectively. The profits are $101. What is each one's share?

How many dollars of capital produce $101 profits?

3. Two men hire a pasture for $45. One puts in 15 cows, the other puts in 12 cows. What should each pay?

4. A and B hire a boat 27 days, B uses it 23 days.

for 50 days, paying $30. A uses it How much should each pay?

5. Our standard gold coin consists of 900 parts gold, 90 parts silver, 10 parts copper. What is the quantity of each metal in 50 pounds of coin?

6. Gunpowder is composed of 15 parts of saltpeter, 2 of sulphur, and 3 of charcoal, mixed together. How many pounds of each are there in 72 pounds of powder?

7. Three farmers hired a threshing-machine for $54. A used it to thresh his crop of 900 bu., B to thresh his crop of 828 bu.; C, 672 bu. How much should each pay?

8. A, B, and C rented a warehouse. A stored in it 2,400 bales cotton; B, 1,500; C, 1,100. A fire destroyed 1,800 bales. How much of the loss should each sustain?

9. X and Y rent a field for $32. X puts in 8 horses for 6 months, and Y 10 horses for 8 months. How many dollars should each pay?

8 horses for 6 months how many for one month?

10 horses for 8 months

=

10. M and N entered into partnership. M puts $200 into the business for 5 months, and N, $300 for 4 months. They gained $132. Find the share of each.

REVIEW DECIMALS.

978. Slate Exercises.

57

1. Express as decimals 5, 10, and 2.

2. .39586.7+ 209.0043 +.81 +3.075 +27.

3. Divide 34,020.072 by 5.309.

570.005= ?

4. Multiply 80.037 by 10.

Seventy-three one hundred-thousandths by one hundred.

.2054 × 1,000 = ?

5. Subtract 48.8067 from 53.07.

.0539 × 26.08 = ?

6. The smaller of two numbers is 8.5307, and their sum is 25.07. Find the larger number.

7. Express .39, 6.175, .00036, and 74.0005 as common fractions (or mixed numbers).

8. Divide .826 by 100; 543.71 by 10,000; and fifty-nine tenthousandths by one thousand.

9. Find the difference between 9.84 and 38.005, and the continued product of 83.09, .734, and 5.007.

10. Reduce 6 shillings 9 pence to the decimal of a pound sterling.

11. Express as decimals seven hundredths, forty-three tenthousandths, and ninety-one millionths.

12. Change, 8, 15, and 6, into decimals. Find their

sum.

13. Express .42796 as a common fraction, and the sum of, 180, and 1878 as a decimal.

14. 3.009 x .07 x .0907.

15. Divide .0075 by .15, and .00044408 by .0112.

16. Divisor, 403.6; quotient, 2.709. Dividend?

18. Change 69 rods to the decimal of a mile.

19. Change .4285 month (30 days) to days, hours, etc.

20. How many meters, each 39.37 inches, in 3 miles 220 rods?

21. Change .1875 bu. to quarts.

22. What decimal of a pound is 13 oz.?

23. Reduce 4 ft. 11 in. to the decimal of a rod.

24. How many links of 7.92 in. each in a 4-rod chain?

25. A chain is 66 ft. What decimal of an acre is 1 sq. chain?