CHAPTER XV.

Ex. 164.

MISCELLANEOUS PROBLEMS.

1. Fifteen men and eight boys together earn $342 a week. If a boy's pay is half a man's pay, what are the daily wages of a man, and also of a boy?

2. A man divides $1622.50 among four persons so that the first has $40 more than the second, the second $60 more than the third, and the third $87.50 more than the fourth. Find the part of the fourth.

3. A family of six persons makes $8.75 a day, and works 304 days in the year. At the end of the year each member of the family puts $80 in a savings bank. Find the daily expense of the family.

4. A man bought 5.5 yds. of cloth for $35. In having a suit made from it, he found that he lacked 1.75 yds., which he procured at the price per yard of his first purchase. What is the cost of the suit if the trimmings cost $6.50 and the making $15?

... 5. A man has 76.25 yds. of linen, worth 44 cts. a yard, made into shirts. It takes 3.05 yds. for a shirt, and the price for making is 50 cts. a shirt. Find the cost of a shirt, and the number he has made.

A man's expenses from the first of January to the end of October 17 are $1845.50. How much must he diminish his daily expense in order that the total expense for the year shall not exceed $2200?!

7. A quart contains 1600 beans of average size, and a field is planted with 22 rows of 800 hills each, with 6 beans in a hill. The increase is tenfold.

What

is the value of the crop at $3 a bushel? (There are 32 quarts in a bushel.)

8. For making 25 gallons of ordinary beer 60 pounds of barley and 0.5 of a pound of hops are needed. If the barley costs $1.50 for 60 pounds, and the hops cost 18 cents a pound, what is the profit to the brewer on a cask of 42 gallons if he sells it for $5 and reckons his labor $1.50?

9. A person receives his income quarterly.

The first

quarter he receives $533.25, the second $1535.20, the third $856.44, the fourth $ 725.19. His expenses for these quarters are respectively $686.60, $734.25, $589.15, $849.65. How much does he save for the year?

10. A hen lays on an average 120 eggs a year worth 24 cents a dozen. She eats a quart of barley every 5 days. The barley is worth 56 cents a bushel. What is the annual profit from this hen?

11. A square garden measuring on each side 40.50 yards is enclosed by three lines of galvanized iron wire. Eight yards of this wire weigh a pound, and it is worth 7.5 cents per pound. What is the cost of the

wire?

12. A family composed of five persons consumes daily one

pound of stale bread for each person, or 1.15 pounds of fresh bread. If bread is worth 5 cents a pound, find the annual saving which this family will make if it eats stale bread altogether.

13. It is estimated that in France 240,000 women and girls are employed in making lace. The annual production has a value of $13,000,000, and the value of the raw material is 0.27 of the value of the lace. Find the average daily wages of these women and girls, supposing that each works 240 days in the year.

14. The salt water which is obtained from the bottom of a mine of rock salt contains 0.09 of its weight of pure salt. What weight of salt water is it necessary to evaporate in order to obtain 4734 pounds of salt?

15. The weight of ashes from the burning of oak wood is 0.03 of the weight of the wood, and the weight of carbonate of potash contained in the ashes is 0.065 of the weight of the ashes. Find the weight of carbonate of potash from 1170 pounds of wood.

16. The weight of sugar from the sugar beet is nearly 0.06 of the weight of the beet. If an acre produces 30,000 pounds of beets that are sold at the rate of $2 a thousand pounds, how many acres of land is it necessary to sow to furnish beets to a sugar factory which produces 150,000 pounds of sugar a year, and what will the be value of the crop obtained?

7. If a workman has taken every day for the last 12 years two glasses of beer at 5 cents a glass, how much could he have saved if he had not indulged this habit, reckoning 365 days each year?!

18. A woman has three children. She pays for each $15 a year for having their clothes made, $1.50 a month. for mending, and $0.35 a week for washing. How much could she save in a year if she knew how to wash, make clothes, and mend?) 539

19. A sheep raiser shears his sheep at an expense of 11 cts. a head. The sheep average 8 lbs. of wool which he sells for 23 cts. a pound. profit after paying for the How many sheep has he?

He finds that his net shearing is $1297.50.

COMMON FRACTIONS.

20. Find the prime factors of 41,580. 21. Find the G.C.M. of 144, 126, 108.

22. Find the L.C.M. of 18, 90, 60, 24.

23. Find the L.C.M. of 14, 35, 343.

24. At 161 cts. a yard. what will 3 yds. of cloth cost? 25. A man has 3763 quarts of berries, which he wishes to put into boxes holding 24 qts. each. How many boxes will be required, and what part of a box will be left over?

26. If a man earns $2 a day, how many days will it take him to earn $100?

27. A lady has 37 qts. of berries to can. If each can holds 2 qts., how many cans of berries will she

have, and what part of another can will there be over?

28. If a man walks 4 miles an hour, how many hours will it take him to walk 40 miles?

29. Some boys wanted a long rope to use on the ice. They made the rope by taking off their sled-ropes and tying them together. The first sled-rope was 2 yds. long, the second 34 yds., the third 27 yds., the fourth 5 yds., and the fifth 3 yds. If the whole length was shortened 1 yds. by the knots, from

tying the sled-ropes together, how long was the rope? 30. A lady bought 34 yds. of cotton cloth, 4 yds. of calico, 16 yds. of flannel, and 12 yds. of gingham. How many yards did she buy in all?

31. A boy went to a store with $5.75 in his purse.

He

bought 34 lbs. of butter at 28 cts. a pound, 131⁄2 lbs. of sugar at 11 cts. a pound, and 11⁄2 lbs. of coffee at 35 cts. a pound. How much money did he have left?

32. Four boys went fishing, and caught 40 trout; the first caught of the whole, the second, and the third 4. How many did the fourth boy catch?

+33.

33.

George has his choice to be one of 3 boys to receive 8 oranges, or one of 4 boys to receive 11 oranges. Which shall he choose?

34. Five girls pick blueberries together; the first picks 7 qts., the second 5 qts., the third 12 qts., the fourth 8 qts., and the fifth 37 qts. How much will they all together get for their berries, at 121 cts. a quart?

35. A farmer puts the following lots of apples into 6 bins: namely, 63 bu., 181 bu., 257 bu., 198 bu., 143 bu., 976 bu., 25 bu. How many bushels will there be for each bin?

COMPOUND QUANTITIES,

36. How many rods are there in 4379 ft. ? r 37. Reduce 9,627,834 ft. to yards, rods, etc. 38. Reduce 96,284 sq. in. to square feet.