Εικόνες σελίδας
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Ηλεκτρ. έκδοση

5. 7-2179083, or 9.2179083. 8. 2.6596926. . 6. 0.7262335.

9. 2.1628630. 7. 0:5682017

10. 1.3322956, or 9.3322956 Art. 168. 1. 0.273603.

5. 0.00003. 2. 0.0536312.

6. 0:772481. 3. 0:0002.

7. 0·0676142. 4. 0·0000000471435.

8. 0.00274074.

SECTION LVIII.

Art. 169.

1st to the 13th inclusive, performed. 14. 151.807.

33. 3.48428. 15. 77190.

34. 0.422838. 16. 324.324.

35. 0.77992. 17. 0·0035991.

36. 0.99285. 18. 7.71707.

37. 0·867362. 19. 3.01182.

38. 0:71254. 20. 3581.242.

39. 0:80818. 21. 4577.626.

40. 1•11204. 22. 49.9336.

41. 0:59905. 23. 5932:52.

42. 0.4809. 24. 4770.1902.

43. 172-002. 0.187295.

44. Performed. 26. 9.33333.

45. 2:3774. 27. 7.1197.

46. 1.1291. 28. 55.54569.

47. 1.9699. 29. 768.575.

48. Performed. 30. 0.0000000243.

49. 7.05. 31. 165.3817.

50. 30.787. 32. 2.236068.

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

25.

n =

Art. 170.
1. Performed.
S-a

log. 1 log. a 2.q=J-1

log. (S-a) — log. (S-2) a+S (9–1); n=

+1.

log. (a +8q-S)— log. a 3, 1=

log. 9 9

log. 1— Jog. (S— S9+19) 4. a=lq-8(9-1); n =

+1.

log. 9 5. S=12285; n =

= 12. 6. q=3; n= =8. 7. I=177147; n = 10. 8. a= 2; n=8.

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 61 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.

SECTION LX.

Art. 173.

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.

B , D 2. 3 yards at 9s.; 5 yards at 7s. 3. 8

years. 4. $8713

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. 64. 20. 40, 20 and 12. 21 Wheat 10s., rye 6s. per bushel. 22. 41 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 $14; 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; C30; D £40. 39. A 6, B 5 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.

32 v

[ocr errors]

Explanation. Let v, w, x, y, and z represent the money of A, B, C, D, and 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 20—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,

- 16 S={S, from which we have
81 S 81. 160

= $81. 160 160 B, in the first game, doubles his money; he will then have 2 w; in the second game he loses S— 2w, and will have left 40 – S. Afterwards his money is doubled three times; he will then have 32 w —88. Hence,

41 S
32 w — 88=} S, and w= $41.

160 In like manner, for C's money we find

21 s
32 x — 48=} S, and x = = $21;

160

V=

=

for D's money,

11 s
32 y-2 S=} S, and y= = $11;

160 and for E's money,

6 S 32% — S=}S, and z=

160

= $6.

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