150. A father left $19275 to his four sons, A, B, C, D, whose ages were 9, 13, 15, 17 years, respectively, to be so divided that the respective parts, at 5% simple interest, should amount to the same sum when they became 21 years of age; what was the share of each?

151. A father willed to his sons, A, B, C, whose ages were 15, 17, 19 years, respectively, $73482, to be divided into three shares, which, at 10% compound interest, would amount to the same sum when they became 21 years of age; what was the share of each?

HIGHER OPERATIONS-VI.

EXERCISE CXXVIII.

525. 152. Extract the square root of 16499844.

153. Extract the cube root of 5088.448.

154. Find the square root of 3.15 to 6 places of decimals. 155. Find 3 to 6 places of decimals.

5

156. Find V1 × V, to 3 decimal places.

14

Х
65

157. Find 1/34 +63 + 81% + 65§., to 2 decimal places. 158. The amount of $700 for 2 yr., interest compounded nnually, is $786.52; find the rate.

159. The compound interest of $800 for 3 yr. is $126.10; what is the rate?

160. What will it cost, at $12 per rod, to fence a square feld whose area is equivalent to that of a rectangular field €4 rd. long and 49 rd. wide?

161. The width of a field is of its length, and its area is 10 acres; what are its dimensions?

162. If each side of a square field were 8 rd. shorter the -rea would be less by 4 acres; what is its area?

163. The volume of a cube whose edge is 36 inches is equal to that of a rectangular block whose dimensions are in the ratio of 3, 2, 13; find the dimensions of the block.

164. How many iron balls 2 in. in diameter will weigh as nuch as an iron ball 10 in. in diameter?

165. Find the cost of a circular field whose circumference -s 125.664 rods, at $5 per acre.

166. A cylinder, 8 inches long, contains 3767 cu. in.; what is the diameter of its base?

167. The length of a rectangular field is 91 rods, and its diagonal is 109 rods; if it were 4 rods wider how much longer should it be to contain 48 acres?

168. If a pipe 6 inches in diameter will discharge a quantity of water in 4 hours, in what time will 3 pipes 4 inches in diameter discharge twice the quantity?

169. Find the number of cubic feet in a room whose dimensions are in the ratio of 51, 4, 3, the distance from a lower to the opposite upper corner being 29 feet.

170. If the minute hand of a clock is 5 inches long, how many inches does its point pass over in 35 minutes?

171. A cubic foot of water weighs 62 b.; how many tons of water will a cistern contain that is 8 ft. 8 in. long, 6 ft. 4 in. wide, and 6 ft. 9 in. deep?

172. A ladder is standing by a wall of equal height, and if the bottom of the ladder be pulled out 10 ft. from the wall it will throw the top of the ladder 2 ft. below the top of the wall; find the length of the ladder

173. A ladder 53 ft. long just reaches a window on one side of a street, and when turned about its foot, just reaches a wall on the other side. If the two positions of the ladder are perpendicular to each other, and the window 28 ft. high, what is the width of the street?

174. Of 5 similar triangles the area of the first is equal to the sum of the areas of the other four; if the altitudes of the latter are 2, 4, 5 and 6 in. respectively, what is the altitude of the fifth?

175. If it requires 500 boards to fence an acre of land, what is the area of a square field which contains as many acres as there are boards in the fence that encloses it?

176. If an iron ball whose diameter is 15 in. be dropped into an upright cylindrical tank whose diameter is 10 ft., how much will the surface of the water be raised?

177. I have an inch board 5 ft. long, 17 in. wide at one end, and 7 in. at the other; how far from the larger end must it be cut straight across so that the two parts shall be equal?

178. The base of a triangular field is 15 ch., and its altitude 12 ch.; how far from the vertical angle must two lines be run parallel to the base so as to divide the area into three equal parts?

179. In the last example, if the land at the vertex is worthless and increases uniformly in value towards the base, how far from the vertex must the two lines be run so as to divide the field into three parts having equal values?

180. A conical piece of maple wood, whose altitude is 10 inches, is floating on the water with its vertex downward; how much of its altitude is above the surface of the water?

ANSWERS.

NOTE.-Answers to problems intended for mental or oral work are not given.

Page 22. Ex. IV. 3. 360. 4. 285. 5. 364. 6. 371. 7. 334. 8. 283. 9.10965. 10. 10154. 11. 2517. 12. 2312424. 13. 1617129. 14. 159. 15. 1413. 16. 182611. 17. 135317. 18. 154625. 19. 64536. 20. 1320. 21. 6885. 22. 9027. 23. 108130. 24. 1280340. 25. $274.92.

Page 23. 26. $2485.91. 27. $10408.86. 28. $280.10. 31. 512. 32. 493. 33. 484. 34. 603. 35. 508. 36. 33314. 38. $9464.40. 39. 7912 mi. 42. 3602990 sq. mi.

Page 24.

40. 48637000.

37. $5385.15.

41. 34884848.

Page 28. Ex. V. 2. 13. 3. 25. 4. 18. 5. 16. 6. 39. 7. 17. 8. 31. 9. 231. 10. 162. 11. 22. 12. 162. 13. 88. 14. 186. 15. 2396. 16. 719. 17. 1575. 18. 4803. 19. 7076. 20. 519. 21. 1223. 22. 1888. 23. 2729. 24. 2985. 25. 4542. 26. 56441. 27. 15536. 28. 436428. 29. $240.51. 30. $74.25. 31. $184.35. 32. $3428.52.

Page 29. 33. $7096.75. 34. $472.25. 35. $107.75. 36. $9999.15. 37. 8214. 38. 7407. 39. 9011. 40. 10479. 41. 8668. 42. 1447888. 43. $76.44. 44. $360.65. 45. $1423.20. 46. $28.35. 47. 1576. 48. $365.88. 49. 578. 50. $4754.35. 51. 1868. 52. $1372.75, 53. 3001. 54. $3998.25. 55. 1026. 56 $156.35. 57. 10746. 58. $25 35. 59. 284. 60. 48. 61. 1732. 62. 1777. 63. $97.75.

Page 30. 64. $9452 50. 65. $1149.20. 66. 245 mi.. 67. 993044. 68. 4 times.

72. 11102 ft.

69. 68. 70. 270. 71. $8281.85.

Page 31. Ex. VI. 2. 560. 4. 2254. 6. 220. 8. 311. 10. 282. 12. 173, 14. 169. 16. 165. 18. 121. 20. 130. 22. 283. 24. 338. 26. $1901.25. 28. $69.15. 30. 567, 370, 646.

Page 32. 32. 6786. 34. 52812. 36. $9187. 38. $23975.

Page 36. Ex. VII. 2. 3025. 3. 6902. 4. 470120.

5. 2922. 6. 18304. 7. 450674. 8. 2925. 9. 60688. 10. 590244. 11. 6336. 12. 34821. 13. 7541469. 14. 3882. 17. 752. 18. 1988. 19. 1904.

15. 43825. 20. 2142.

16. 4484139.

Page 37. 22. 1260. 23. 8640. 24. 170500. 25. 1632. 26. 14476. 27. 1036800. 28. 6256. 29. 52325. 30. 1556856. 31. 2923. 32. 59940. 33. 5619501. 34. 26645. 35. 119109094835. 36. 21053. 37. 594731545. 38. 24336. 39. 475065601536. 40. 4888. 41. 213255462816. 42. 59784. 43. 114879044530. 44. $5440. 45. $276.66. 46. $10658. 47. $15547.68. 48. $167491.80. 49. $573806.25. $3996.75. 51. $107.52. 52. $470.08.

Page 38. 53. 57810. 54. $151272.

57. 6246. 58. 18648.

50.

55. 91289796 mi.

59. 28518. 60. 28350. 61. 47817.

62. 92016. 63. 8008. 64. 5845. 65. 1665.

Page 39. 67. 4700. 68. 863000. 69. 5040. 70. 90250000. 71. 1300. 72. 137000. 73. 17000. 75. 840000. 76. 4380000. 77. 140700000000. 78. $6000000. 79. 342000 ft. 80. 52290000.

Page 40. 82. 3393. 83. 4361875. 84. 58114. 640065987. 86. 3366. 87. 479040. 88. 1640967768.

85.