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5. I-2179083, or 9-2179083. 8. 2·6596926.

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51. Progression 7, 8.6394, 10-662, 13-16, 16-242, 20

ART. 170.

1. Performed.

S-a

2. q=

n=

3. l =

log. l-log. a

8-1 log. (S-a)-log. (S-1)
a+S (q-1)
+8 (q − 1); n =

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4. a-lg-S(q—1); n=

5. S=12285; n = 12.

6. q=3; n=8.

7. 7=177147; n = 10.

8. a=2; n=8.

log. (a+Sq-S)-log. a +1.

log. q

log. l—log. (S—Sq+lq) +1.

log. q

SECTION LIX.

ART. 171.

1st to 5th inclusive, performed.

6. $569.801.

7. $1948.67.

8. $333.24.

9. $1829-71.

10. $250.

11. 14.137 years, or 14 years, 1 month, 29 days. 12. 0·06085, or 6 per cent. nearly.

13. 11.8956 years, or 11 years, 10 months, 22 days. 14. 18.854 years, or 18 years, 10 months, 7 days. 15. 14-2067 years, or 14 years, 2 months, 14 days. 16. $644-781.

17. 83310.

18. 0.03205.

19. 26.91 years, or 26 years, 10 months, 28 days. ART. 172.

1. Performed.

2. $3558-094.

ART. 173.

SECTION LX.

1st 2d and 3d performed.

4. $7686-22.

5. $7857.98.

6. $1169.84.

7. 19-387 years, or 19 years, 4 months, 19 days.

MISCELLANEOUS QUESTIONS.

1. A $948, B $1896, C $2844, D $4740.

2. 3 yards at 9s.; 5 yards at 7s.

3. 8 years.

4. $8714.

5. 60 years.

6. 55.

7. 4 days.

8. 20.

9. Breadth 30, length 40 rods.

10. 10 eagles; $30.

11. A $60; B $48.

12. $1000.

13. $50.

14. $400, $500, $700.

15. 800 men.

16. $20.

17. £280.

18. 14 beggars; 32s.

19. 62.

20. 40, 20 and 12.

21 Wheat 10s., rye 6s. per bushel.

22..

23. 23.

24. 21 and 16.

25. 17 and 8. 26. 24s.

27. 53.

28. A $20; B $50.

29. Greater 79; less 35. 30. A $300; B $350.

31. Length 20, breadth 18 feet

32. A $1; B $1; C $2. 33. 15 and 12.

34. 10 and 8.

35. 12 and 19.

36. 8 and 15.

37. 40 sheep.

38. A £10; B 20; C £30; D£40.

39. A 6, B5 miles per hour.

40. 93.

41. 8 hours.

42. 6 hours, or 31 hours.

43. 3 and 243.

44. A 204, B 200 acres.

45. 5 and 4.

46. 36 and 24.

47. Breadth 100, length 150 feet.

48. 12 and 10.

49. Breadth 40, length 50 rods.

50. 16 and 9.

51. 6 and 4.

52. 18 and 6.

53. 3 and 5.

54. 5 and 9.

55. 81 scholars.

56. 23.

57. Depth of 1st 4 feet, that of 2d 5 feet.

58. 8.

59. 25.

60. Court 30 by 19 feet; height of fence 4 feet.

61. 12 yards.

62. 150 miles.

63. 25.

64. A $200; B $300.

65. 9 and 15.

66. 741.

67. A $81; B $41; C $21; D $11; E $6.

Explanation.

and

Let v, w, x, y, and z represent the money of A, B, C, D, E, respectively, when they began to play; and let S represent the known amount of their money, which is 5. 32 or $160.

In the first game A loses the whole amount minus his own share, or S-v; he will therefore have left v— (S— v), or 2v-S. After this his money is doubled four times; he will then have 32 v - 16 S; this must be equal to $32 or S. Hence,

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B, in the first game, doubles his money; he will then have 2w; in the second game he loses S-2 w, and will have left 4w-S. Afterwards his money is doubled three times; he will then have 32 w-8 S. Hence,

[blocks in formation]

32z-SS, and z =

=

$6.

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