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 3 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.?

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

976. Admission to N. Y. State Normal Schools.

1. Express in words:

(a) 3,050,050,813; (b) 50,002.004; (c) $10,103,042.5075; (d) 103.75 per cent; MDCCCLXXXVIII.

2. Find the sum of all the prime numbers to 50.

3. If A and B can mow a field in seven days; and A, B, and C mow it in five days, for $25, what ought C to receive?

4. With 5 bushels of wheat, at 80 per bushel, and 5 bushels of rye, at 60 per bushel, how many bushels of oats, at 30 per bushel, must be added to make a mixture worth 50¢ per bushel?

x = number. Mixture contains (x + 10) bu. @ 50 %.

5. To of a score add of a dozen, and from the sum subtract of a hundred. What is the remainder?

6. What must be the length of a load of wood that is four feet wide, and five and one-third feet high, to contain two cords?

x = length.

7. Bought a hogshead of molasses containing 128 gallons, at 65 a gallon; paid 80 for cartage, and lost 16 gallons by leakage. At what price per gallon must the remainder be sold to gain one-fifth of the entire cost?

8. What is the least number that will exactly contain 48, 20, 21, 24?

9. Find the least common multiple of 24, 44, 65, 100.

10. Sold 50 sofas for $2,250. 25 of them were sold at a gain of 20 per cent, and 25 at a loss of 20 per cent. What was the gain or loss on the transaction?

11. Bought a number of eggs, and sold 11 of them for what 18 cost me. What was my gain per cent?

12. A bookseller wishes to mark up the price of a book which he is now selling for $2, so that he can deduct 15 per cent, and yet receive the present price. What must be the marked price?

13. What is the difference between .75 divided by 75, and 75 divided by .75?

14. A pole extended into the mud 55 feet; of its length was in the river, and of it in the air. What was the length of the

pole?

x = length.

15. Find the exact amount of $68, from March 13 to June 15, interest 6 per cent.

1888,

Take 366 days to the year.

16. How many acres in a field 210 ch. long and 50 ch. wide?

17. It took 9 horses to move a stick of timber weighing 12,590 lb. How many pounds would a stick weigh that would take 7 horses to move?

18. Mr. A sold a horse for $275, which was 5 per cent less than he asked for it, and his asking price was 5 per cent more than the horse cost him. What was the cost of the horse?

19. Write in Roman numerals 1889.

20. A man purchased a rectangular field 18 rods wide, containing 10 acres 146 square rods of land. The land cost him $80 per acre, and he surrounded it by a fence costing 80 per rod. How much did the land cost, and how much the fence?

21. By selling a carriage for $117, a dealer lost 10 per cent of its cost. For how much should he have sold it to gain 10 per cent of its cost?

22. A man, dying, left of his estate to his wife, of the remainder to his son, and the remainder to his daughter, who received $5,000. What was the value of the estate, and what was the son's share?

X= value of estate.

23. What is the interest of $10, for 10 years 10 months and 10 days, at 10 per cent?

24. If it takes one man 7 days to do a piece of work, how long will it take 3 men to do 23 times as much?

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?