ART. 170. 1. Performed. S-a 2. q= n= 3. l = log. l-log. a 8-1 log. (S-a)-log. (S-1) 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, 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, 32z-SS, and z = = $6. |