3. How many sq. ft. of lumber necessary to board the gable ends of a barn, each end being 24 ft. wide, 20 ft. high to the eaves, 28 ft. high to the ridge pole? 4. What is the area of a quadrant whose radius is 4 ft. ? 5. The slant height of a cone is 24 inches, the diameter of its base 12 in. What is the diameter of a sphere having an equivalent volume?

6. How many square miles on the surface of an asteroid 300 miles in diameter?

7. If an aperture an inch square be plugged with a round plug an inch in diameter, what area will remain open? 8. How many sq. ft. in the exterior surface of a spire in the form of a hexagonal pyramid 100 ft. high, each side of base 4 ft. ?

9. A square pyramid 270 ft. high contains 14520 cu. yds. What is the length of one side of base?

10. What are the relative diameters of a 27 lb. cannon ball and a 64 lb. cannon ball ?

11. Two square fields

contains 33 acres.

12. Find the area of

have the ratio 3: 5. The smaller Find length of side of larger field.

one side of a cubical mound whose volume is equal to the volume of another mound 288 ft. long, 216 ft. broad, 48 ft. high.

13. How many globes of gold, each 5 inches in diameter, weigh as much as one of the same material 15 inches in diameter?

14. A cone 3 feet high contains 1539 cu. ft. What is the volume of a similar cone 5 ft. high?

15. Find the ratio of the surfaces of two spheres whose diameters have the ratio 6 to 7.

CHAPTER XVI.

MISCELLANEOUS EXAMPLES.

1. The sum of two numbers is 2836; their difference is 987. What are the numbers?

2. The sum of four numbers is 4987; three of the numbers are 1820, 529, and 2417. What is the fourth number?

3. The product of three numbers is 4375; two of the numbers are 7 and 25. What is the third number? 4. At an election the total number of votes cast for two candidates was 8136. The successful candidate was elected by a majority of 590 votes. How many votes did each receive?

5. Find the product of the prime factors of 21, 52 and 95.

6. Find the product of the prime factors common to 84, 126 and 252.

7. At what price per barrel can flour be purchased by

different persons using respectively $54, $228, and $138, so that each may purchase an exact number of barrels ?

8. What is the least number of years that may be divided into either 42 years, 96 years, or 180 years?

9. What is the smallest number of marbles that can be distributed equally among 9, 21, or 25 boys?

10. A farmer sold 10 loads of wheat, each load containing

16 bags of 3 bushels each, valued at 90c. per bushel. He received in payment woolen cloth, worth $1.50 per yard. How many yards did he receive?

11. How many acres in a farm which consists of 5 fields containing, the first 1243 acres, the second 495 acres, the third 96 acres, the fourth 108 acres, the fifth 825 acres?

12. If the farm described in Ex. 11 were divided into 3 equal fields, how many acres would each contain? 13. 21 is one half of what number? Is one third of what number?

14. The sum of two numbers is 1263; the smaller number is one half of the greater. What is the greater number?

15. Find cost of 3273 cords of wood at $5 per cord. 16. Find cost of 1 ton of hay if 28 tons cost $2433. 17. Paid $5973 for a lot, and sold it so as to lose of what was paid. For what was the lot sold?

18. How many yards of muslin worth 8 c. per yard, can be bought for $7.25 ?

19. How many miles will a vessel sail in 36 hours, averaging 75 miles per hour?

20. Having a farm worth $3250, I sold part of it for $812.50. What was the value of the part sold compared with the value of the farm? Compared with the value of the part that remained ?

21. A man expended $59, which was

How much money had he remaining ?

of his money.

22. A man expended $59, which was of his money. How much money had he remaining ?.

23. A man owning of a vessel, sold of his share for $2910. What was the value of the vessel, at the same rate of valuation?

24. How many thirds in 3?

25. If I spend of my money, and lose of it, what part have I left ?

26. If I spend

of my money, and lose of the remain

der, what part have I left ?

27. I spent

and

of my money, and then had $22.

How much had I at first?

28. If 6 men can do a piece of work in 4 days, in how

many days can 4 men do it?

29. The difference between

How much has he?

and 3 of A's money is $98.

30. of a dollar is what part of 37 cents ?

31. Add 175 units, 175 tenths, 175 hundredths, 175 thou

sandths.

32. From one hundred subtract 135

hundredths.

33. Divide the cube of 12.5 by the square of 6.35.

35. What common fraction equals .1+.125+.31?

36. The product of two factors is .0625. One of the factors is 1.25; what is the other?

37. The divisor 5.125 is 5 times the quotient. What is the dividend ?

38. What is of expressed decimally?

39. Find sum of .3, .36 and .81 expressed as a common fraction.

40. What is .25 of .5 of $32040.96 ?

41. Find cost of laying mile of sidewalk, at $.62 per linear foot.

42. Find cost of laying a sidewalk of a mile long, 6 feet wide at 12 cents per square foot.

43. Find cost of building a wall 120 feet long, 13 feet thick, 8 feet high, at 15 cents per cubic foot.

44. How many square feet on the surfaces of a block of stone, 8 feet long, 4 feet wide, 2 feet thick?

45. From a pile of stone measuring 40 feet long, 12 feet high, 20 feet wide, 15 loads are taken, averaging 1

cubic yards each load. How many cubic feet of stone remain in the pile?

46. What is the difference in square feet between 25 feet square and 25 square feet?

47. How many bushels will a bin contain which is 15 feet long, 12 feet high, 9 feet wide?

48. How many gallons will a vat contain which is 11 feet high, 7 feet long, 6 feet wide?

49. How many quarts in .75 of a bushel ?

50. What decimal of a cubic foot are 108 cubic inches?

51. Find cost of 12300 bricks, at $7.50 per M.

52. How many yards of carpeting,

yard wide, are required to cover a floor 12 feet by 18 feet? 53. Mr. J. buys the N. of S. E. 4 of Sec. 30, T. 7 N. R. 5 E., etc., at $5.25 per acre. How much does he pay? 54. A ship's chronometer shows a gain of 1 h. 20 m. How many degrees has the vessel sailed? E. or W. 55. What part of a circumference is an arc of 11° 15′ ? o. How many perches of stone in a quarry 4950 feet long, 200 feet wide, if the stone is 24 feet deep? 57. Find value, at $3.25 per cord, of a pile of wood 320 feet long, 4 feet wide, 8 feet high.

58. What is the value of 8 lb. 3 oz. 16 pwt. 14 gr. of gold, at $15.85 an ounce?

59. From .9 of a day subtract of a week.

60. How many barrels of water, 30 gallons each, have fallen on an acre of land, during a rain fall of 14 inches?