17. A boy, having some money, earned twice as much and $.48 more, when he had $9.78. How much did he earn ?

18. One third of a sum of money exceeds one fourth of the sum by $17. What is the sum?

19. Two fifths of a number is 14 less than five ninths of the number. Find the number.

20. 2 times a certain number is greater by 45 than three fourths of the number. Find the number.

21. Divide 176 into four parts so that the first shall be four times the second, the third one third of the second, and the fourth one half of the first.

HINT. — Let x = the third part.

22. The sum of three numbers is 1658. The second exceeds the first by 130, and the third exceeds the first by 79. Find the three numbers.

23. Three numbers, when added, amount to 11.89. The second exceeds the first by 3.28 and the third exceeds the second by 1.37. Find them.

24. A farmer has apples, potatoes, turnips, and onions in his cellar. The number of bushels of apples is 13 less than the number of bushels of potatoes; the number of bushels of turnips is 19 less than the number of bushels of apples, and there are 3 more bushels of turnips than of onions. The entire quantity is 72 bushels. Find the number of bushels of each.

25. In a certain class, the number of girls who received honor marks was three more than twice the number of boys who received honor marks. The number of honor pupils was 18. How many were girls, and how many were boys?

26. Seven times a certain sum of money plus $18 is equal to five times the sum plus $50. What is the sum of money?

476. Oral

REVIEW AND PRACTICE

1. Name the prime numbers from 1 to 100.

2. How may we know, without trial, that 723,468 will not exactly divide 398,650,076,341 ?

3. There are two decimal places in one factor, three in another, one in another, and four in another. How many decimal places are there in the product of the four factors? 4. If one fifth of an acre of land is worth $20, what is one twentieth of an acre worth at the same rate?

5. 48 x 25? 57 x 99 = ?

560 x 125=? 6. 6125? 33125? 17.331=? 7. 360 x.16? 39.25=? 150÷.2=? 8. 63 × 331=? 99 × 663 = ? 42 × .142 = ?

9. 50 +5 × 2 ? x =

10. 20% of 331%

=

88-8÷4=? 7x8+16 ÷ 4 = ?

what common fraction?

11. Two successive trade discounts of 10% are the same as what single discount?

12. Test each of the following numbers for divisibility by 2, 3, 4, 5, 6, 8, and 9:

a. 2364

b. 486,728

c. 72,056,391 d. 91,307,865

e. 42,836,076 f. 90,010,332 g. 8,705,637,411

13. If a man earns $99 in 17 days, how much will he earn in 51 days at the same rate?

14. What is the least number that will exactly contain 2, 3, and 4?

15. What is the greatest number that will exactly divide 60, 96, and 132?

16. What is the cost of 7000 shingles at $5.50 per M?

17. What is the cost of 1500 lb. of mixed feed at $1.80 per cwt.?

18. Two long tons contain how many more pounds than two short tons?

19. What is the length of a solar year?

20. How many grains are there in 5 lb. Avoirdupois ?

21. A quart of spirits of camphor will fill how many 4-ounce bottles?

22. What is the area of a triangle whose base is 2 ft. and whose altitude is 20 in. ?

23. What is the altitude of a parallelogram having an area of 96 sq. in. and a base of 2 ft.?

24. A piece of lumber 2" by 4", and 6 ft. long, contains how many board feet?

25. a. How many shingles are required for 1 square foot of roof, when they are laid 6 inches to the weather?

b. How many are required for one square of roofing?

26. What is the cost of a slate roof 20' x 30' at $10 per square?

27. A grocer sold 663 % of a hogshead of vinegar. How many gallons did he sell?

28. 331% of a rod is how many feet?

29. What per cent does a grocer gain on celery bought at 30 a dozen heads, and sold at 5¢ a head?

30. What per cent does a merchant gain when he sells two yards of cloth for what three yards cost?

31. A newsboy bought 30 papers and sold them at a profit of 50%. How many papers can he buy with the money received for the papers sold?

32. How much commission does an agent receive for selling $1200 worth of goods, when the rate of his commission is 163%?

33. What is the premium for insuring a $10,000 stock of goods for one fourth of its value at 2% ?

34. Mr. Wheelock's county tax was $75 when the county tax rate was 5 mills on a dollar. What was the assessed valuation of Mr. Wheelock's property?

35. A tax collector's suretyship bond cost him $28, at the rate of $4 per thousand. What was the amount of his bond?

36. On a certain day, New York exchange sold in Kansas City at % premium. What was the premium on a $16,000 draft?

37. When exchange on London is quoted at 4.871, what is the cost of a draft for £100?

38. When exchange on Geneva is quoted at 5.20, what is the cost in Philadelphia of a draft on Geneva for 104 francs? What is the face of a draft that $100 will buy?

39. What is the face of a Berlin draft that can be bought for $240 when exchange is quoted at 96?

40. A room 12 meters long is how many feet long? (Think all the way through before you perform any operation.)

41. 300 liters of oats are about how many bushels?

42. 100 liters of kerosene oil are about how many gallons?

43. About how many square meters of carpet are required to cover a floor 2 rods wide and 4 rods long?

44. What is the scale of linear measure in the metric system? Of surface measure? Of volume measure?

45. State your weight approximately, in kilograms.

477. Written

Solve the following problems, using equations wherever they will shorten or simplify the work:

1. Find (a) the greatest common divisor, and (b) the least common multiple of 126, 210, 294, and 462.

3. Kerosene is 80% as heavy as water. If a gallon of water weighs 83 lb., how many gallons are there in a ship load of kerosene weighing 3900 tons?

4. In 1890 there were 166,706 miles of railroad in the United States, and in 1900 there were 190,082 miles. What was the per cent of increase?

5. The copper cent, which has not been coined since 1864, weighed 72 grains and was composed of 88% copper and 12% nickel. How many pounds, Avoirdupois, of copper were there in $100 worth of those coins?

6. Find the number of gallons of water that can be contained in a rectangular cistern 7 ft. by 12 ft. by 51 ft,

7. On the 29th day of April, 1908, Francis Burns bought of Fred J. Peck, 9 tons of egg coal and 5 tons of chestnut coal at $6.10 per ton, and 2 tons of pea coal at $4.25 per ton. Make out the bill and receipt it as the creditor's agent.

8. A boy spent of his money, earned 65 cents, and then had ğ of his original sum. How much money had he at first? (Let the money he had at first.)

x =

9. A man owning 135 acres of land, sold 63 A. 87 sq. rd. How much land had he left?

10. Add 40° 37' 19, 20° 40' 30", and 9° 30′ 45′′.

11. Divide 35° 21′ 30'' by 15.