CASE XVII.

Time Problems, Second Class.

1. What time after 2 o'clock are the hour and minute

hands of a clock together?

SOLUTION.-The minute-hand gains on the hour-hand 12-1, or 11 spaces, in going 12 spaces; hence to gain 1 space it must go of 12 spaces, which is 17, or 111 spaces, and to gain 2 spaces, the distance they are apart at 2 o'clock, it must go 2 spaces, which requires 101 minutes; hence the time is 101 minutes past 2.

2. At what time between 4 and 5 o'clock are the hour and minute hands of a watch together? Ans. 21 min. past 4. 3. At what time between 7 and 8 o'clock are the hour and minute hands of a watch together? Ans. 38 min. past 7. 4. In how many minutes after 4 o'clock will the hour and minute hands be 5 minute-spaces apart?

Ans. 16 min.; 27 min. 5. In how many minutes after 4 o'clock will the hour and minute hands be 5 minutes of time apart?

Ans. 16 min.; 26 min.

CASE XVIII.

Age Problems, Second Class.

1. A's age is 4 times B's age, but in 10 years be 2 times B's age; required the age of each.

SOLUTION.-By the first condition of the problem, 4 times B's age equals A's age, hence the difference of their ages is 3 times B's age, and once B's age equals of the difference of their ages; in 10 years, 2 times B's age equals A's age; hence B's age then equals the difference of their ages. Therefore, 10 years is the difference between of the difference of their ages, and the difference of their ages, or of the difference of their ages; and, or the difference of their ages is of 10, or 15 years. If 3 times B's age, which equals the difference of their ages, equals 15 years, B's age is of 15 years, or 5 years, and A's age is 4 times 5, or 20 years. 2. C is 4 times as old as D, but in 12 years C will be 3 times as old as D; how old is each? 3. R is as old as S, but in 14 years he will be as old; Ans. R's, 14 yr.; S's, 42 yr.

Ans. 24 yr.;

96 yr.

what is the age of each? 4. Six years ago when I first met Mr. Wilson I was as old as he, but now I am as old; what is the age of each? Ans. My age, 18 yr.; Mr. W's, 54 yr.

SECTION XIV

MISCELLANEOUS PROBLEMS.

These problems are designed both to test the pupils' knowledge of the
subjects studied and their powers of reasoning. They afford a good
review of the work, and are to be used according to the needs of the
pupil and the judgment of the teacher.

1. Find the greatest common divisor of 847, 1331, and
1573.
Ans. 121.

2. Find the least common multiple of 78, 156, 260, and
520.
Ans. 1560.

3. What is the value of ++ diminished by +}+
20?
Ans. 1.

4. What is the value of +17-18 divided by +- ?

Ans. 17.

5. Find the value of 15×17×18 divided by 8×1

Ans. 1.

6. What part of 33 is 23? Of 7g is 5? Ans. 18; 1.

14. What number, when multiplied by (50-100+

will give the product 13,18?

7

4

Ans..

19. How many dollars in £24 16 s. 9 d.? 20. How many pounds Troy are there A voirdupois?

Ans. $120.87.

in 432 pounds Ans. 525 lb.

Ans. 616 gal.

21. In 752 gallons of wine measure how many gallons of the old beer measure? 22. How many days from January 1st, 1860, to January 1st, 1885? 23. On what day of the week did the 19th century begin? Ans. Thursday.

Ans. 9132.

24. If a telegram is sent from Philadelphia, 75° 9' 5" W. long. to San Francisco, 122° 26' 15" W., at 9 h. 30 min. P. M., at what hour will it be received at the office in San Francisco? Ans. 6 h. 20 min. 51 sec. P. .M. 25. A turnpike 40 ft. wide was run through a township; now many acres per mile did it occupy ? Ans. 43 A.

26. Mr. Jones has a cylindrical cistern 8 ft. 6 in. in diameter, and 5 ft. 9 in. deep; how many hogsheads of water does it contain? Ans. 38.74+ hhd.

27. The house to which the above cistern belongs is 40 ft. long and 34 ft. wide, the eaves projecting 6 in. on each side, and all the water falling on the roof is conducted to the cistern; to what depth would it be filled by a shower in which of an inch of rain falls, and how many inches of rain would fill the cistern? Ans. 1 ft. 10+ in 248 in.

28. 295 is 62% of what number?

Ans. 472. 29. What is 33% of 41; also % of ? Ans 11; Ho 30. A lady lost $750, which was 25% of what she then had; how much had she at first? Ans. $3750. 31. What per cent. of 3 is ; and what per cent. of 35 is 18? Ans. 163%; 25%. 32. What is the interest on $680 for 5 yr. 10 mo. 12 da at 7 per cent.? Ans. $279.25. 33. What principal will in 5 yr. 10 mo. 15 da., at 6%, give $456.84 interest? Ans. $1296. 34. In what time will $4080, at 5 per cent., give $668.10 interest? Ans. 3 yr. 3 mo. 9 da. 35. At what per cent. will $9876, in 6 yr. 2 mo. 12 da., give $5510.808 interest? Ans. 9%. 36. What are the contents in liquid measure of a tin pan, whose height is 5 inches, upper diameter 17 inches, and lower diameter 9 in.? Ans. 274+ gal.

37. I have a bin 8 ft. 3 in. long, 3 ft. 6 in. wide, and 4ft. 9 in. deep, filled with corn in the ear; how many bushels are there (Art. 371, note), and how many bushels when shelled, if 2 bushels on the ear make 1 bushel when shelled? Ans. 8738 bu.; 43,8 bu.

89

38. What is my annual rate of profit on a ten-acre woodlot, which cost $100, the yearly growth of wood averaging 1 cord to the acre, and the market price $4.25 a cord, the cutting and hauling costing 759 a cord? Ans. 35%.

39. I have a yard 100 feet square, which I wish to pave, making a flagged walk 6 ft. wide around the outside at 75% a square yard, and paving the rest with bricks at $9 M., allowing 4 bricks to the square foot; what will be the whole cost? Ans. $466.78.

40. Mr. Snyder has a garden containing 1 acres, whose width is 180 ft.; it is enclosed with a brick wall 8 ft. 6 in. high and 9 in. thick, in which there are 2 doors, each 6 ft. 3 in. by 4 ft., and a gateway 12 ft. wide; what will be the cost of the wall at $10 M. for the bricks, and $2 p M. for the labor? Ans. $1698.746

41. A sold 20% of his land to B, and 25% of the remain der to C, and then had 120 acres; how much had he at first? Ans. 200 acres.

42. A man bought 40 shares of stock, which is 25% of what he already had; now if he sells 80 shares, the remainder is what per cent. of his first number? Ans. 75%. 43. The sum of A's and B's money is $2800, and 25% of A's equals 33% of B's; how much has each?

Ans. A, $1600; B, $1200. 44. A sold two dwellings for $3600 each; on one he gained 20%, and on the other he lost 20%; what was his gain or loss? Ans. Loss, $300. 45. Cynthia's money is 25% more than Florence's money; then Florence's money is how many per cent. less than Cynthia's?

Ans. 20%.

46. Miss Poole sold her piano for $360, and cleared of this money; what % would she have gained by selling it for 5% more than she received? Ans. 26%..

47. A man owns 80 shares of bank stock, at $50 each; the company declares a 5% dividend, payable in stock; how many shares will he then own? Ans. 84 shares.

48. Mrs. Clark receives $300, payable in stock, as her share of a 4 per cent. dividend; how many shares, at $50 each, will she then own? Ans. 156 shares.

49. Mrs. Davis received 10 shares and $45 in money as her share of a 5% dividend; how many shares, at $50 each, did she then own? Ans. 228 shares.

50. Miss Willard sold her house and lot for $5000, receiving as much for the house as the lot; on the lot she gained 4 per cent. and on the house lost 4 per cent.; what was the gain or loss? Ans. No gain or loss.

51. A sold B 40 sheep, which was 50% of what B already had and 25% of what A had remaining; A afterward sold B 40 more; now what per cent. of B's number equals A's number? Ans. 75%.

52. William gave 80 words to Mary to spell, which was 66% of the number Mary gave William: now if she had