QA y UC-NRLF KEY TQ EXAMPLES FOR PBA.CTICE WRITTEN ARITHMETIC. FOR THE USE OF TEACHERS. BY FREDERIC A. ADAMS, PRINCIPAL OF DU.MMEK ACADEMY. CO L W E L CQ PUBLISHED BY DANIEL BIXBY.. 1-847. REESE LIBRARY OF IHF UNIVERSITY OF CALIFORNIA. /rU2*Zis^ /,v Accessions Nc. .^.A.?> Shelf No. . * > KEY TO EXAMPLES FOE PRACTICE IN WRITTEN ARITHMETIC. FOR THE USE OF TEACHERS. BY FREDERIC A. ADAMS, PRINCIPAL OF DUMMER ACADEMY. v v OF THE * LOWELL: PUBLISHED BY DANIEL BIXBY. 1847. Entered according to Act of Congress, in the year 1846, BY DANIEL BIXBY, In the Clerk's Office of the District Court of the District of Massachusetts. Stereotyped and Printed By Samuel N. Dickinson & Company, 52 Washington St Boston. TO TEACHERS. IT is essential to the pupil's progress that he be required to master thoroughly each principle in the First Part, before he attempts to solve the questions that come under it in the Second. In this way alone can he proceed intelligently and pleasantly in his work. In no instance in the Key is the process of the solution given, but only the resulf. The few suggestions that are made, in connection with some of the more difficult examples, are designed only as hints, to stimulate and encourage the student ; not to supply the place of study on his part. No question is given, the solution of which is riot provided for in the principles and rules which the Arithmetic contains. DUMMER ACADEMY, September 16, 1846. KEY TO WRITTEN ARITHMETIC. SECTION I. 1. 1314. 2. 1442. 3. 2068. 4. 2134. 5. 937. 6. 2278. 7. 2063. 8. 2145. 9. 1846. 10. 2364. 11. 2443. 12. 2594. 13. 1582. 14. 21941. 15. 17102. 16. 6495. 17. 6262. 18. 6522. 19. 6650. 20. 23434. 21. 15708. 22. 16060. 23. 18033. 24. 11957. 25. 18739. 26. 2234842. 27. 6313374. 28. 4284811. 29. 4055313. 30. 16888340. 31. Performed. 32. 12478. 33. 23928. 34. 215140. 35. 569069. 36. 761973. 37. 371897. 38. 1274915. 39. 62784. 40. 358915. SECTION II. 1. 383. 6. 555. 2. 92. 7. 195. 3. 215. 8. 20. 4. 80. 9. 117. 5. 182. 10. 750. KEY. 11. 417. 29. 57 years. 12. 71. 30. 101620. 13. 4082. 31. 102018. 14. 1894. 32. 51447. 15. 1751. 33. 86921. 16. 688. 34. 127291. 17. 110. 35. 412863. 18. 177. 36. 545796. 19. 826. 37. 510313. 20. 1464. 38. 350674. 21. 58403. 39. 356469. 22. 214514. 40. 581564. 23. 623217. 41. Performed. 24. 86201. 42. Performed. 25. 5642. 43. 165. 26. 128 years. 44. 276. 27. 156 years. 45. 1388. 28. 44 years. 46. 1542. SECTION III. 1. Performed. 20. 357838. 2. 11764. 21. 31044114. 3. 47478. 22. 253296936. 4. 37088. 23. 639107315. 5. 75166. 24. 677282208. 6. 45496. 25. 11744226. 7. 83835. 26, 2788998514. 8. 90972. 27. 622233540. 9. 216335. 28. 286616918. 10. 559322. 29. 53072684. 11. 711648. 30. 2331512816. 12. 174262. 31. 836626937432. 13. 761940. 32. 59933126820. 14. 389408. 33. 764183400522. 15. 328287. 34. 122162496384. 16. 3378219. 35. 406478903992. 17. 8330688. 36. 464003894669. 18. 2764557. 37, 7500. 19. 246694. 38. 45375. KEY. 39. 40140. 45. 17521556. 40. 36015. 46. 2272392510. 41. 9125. 47. 469580064. 42. 755232. 48. 321354. 43. 88960. 49. 18653328. 44. Performed. SECTION IV. 1. Performed. 21. 71 barrels. 2. 346. 22. 16-f 21793. 3. 579. 23. 98+2699. 4. 976. 24. 37+39467. 5. 825+41. 25. Performed. 6. 376. 26. 192877. 7. 345. 27. 49459+5. 8. 798. 28. 23853+4. 9. 5279. 29. 85527+3. 10. 52672+79. 30. 2410069+3. 11. 14+63. 31. 24451677+1. 12. 20605+31. 32. 103978+4. 13. 4292+17. 33. 163684+9. 14 2074+66. 34. 1172845+2. 15. 120899+18. 35. 2231+2. 16. 104683+10. 36. 3129+8. 17. 14793419+16. 37. 5108+15. 18. 2224+12. 38. 4365+9. 19. 22947+24. 39. 30629+7. 20. 7157 dollars. Miscellaneous Examples. 1. 5109 dollars. 6. 994 dollars. 2. 186 dollars. 7. 216 dollars. 3. 1674 dollars. 8. 192 dollars. 4. 647 dollars. 9. Lost S34.00. 5. Whole amount, $3297; 10. $180.00 more than his each barrel, $5^. salary. 8 KEY. SECTION V. 1. 9 feet. 2. 126 feet. 3. 48 inches. 4. 204 inches. 5. 1584 inches. 6. 576 inches. 7. 756 inches. 8. 1351 inches. 9. 1984 inches. 10. 213 inches. 11. 396 feet. 12. 1435 feet. 13. 112266 inches. 14. 119ifeet. 15. 6168 inches. 16. 2620 shillings. 17. 15620 shillings. 18. 15160 shillings. 19. 228 pence. 20. 1812 pence. 21. 34036 pence. 22. 4188 farthings. 23. 232 ounces. 24. 1501 ounces. 25. 5031 pounds. 26. 30520 pounds. 27. 857 pennyweights. 28. 3174 pennyweights. 29. 2304 grains. 30. 38140. 31. 216 pints. 32. 1818 quarts. 33. 2016 gills. 34. 5568 quarts. 35. 4672 pints. 36. 7392 quarts. 37. 1872 square inches. 38. 22869. 39. 509652. 40. 37298J square feet. 41. 14751 square feet. 42. 29376 solid inches. 43. 910656 solid inches. 44. 32760 solid inches. 45. 781 solid feet. 46. 3484 solid feet. 47. 5773 solid feet. 48. 375 quarters. 49. 315 quarters. 50. 3108 nails. 51. 427 J inches. 52. 4176 nails. 53. 24634^- feet. 54. 1128600 inches. 55. 5247 pence. 56. 960 sixpences. 57. 3806 sixpences. 58. 3620 threepences. 59. 5040 fourpences. 60. 28 times. 61. 112 parcels. 62. 51fk times. 63. 19200 acres. 64. 480000 acres. KEY. SE CTION VI. 1. 17 8s. 2. 250. 3. 684. 4. 46. 5. 47 Is. 6. 84 5s. 7. 5 17s. Id. 8. 16 19s. 9. 6 17s. 3d. 10. 243J s. 11. 74 days. 12. 576 d. 17 h. 13. 1364 days, 50 m. 14. 6236 h. 56m. 29 sec. 15. 30 gals. 1 pt. 16. 2646 gals. 17. 215|f bis. 18. 433 pks. 5 qts. 19. 1506bu.2pks.7qts.lpt. 20. 120 bu. 6 qts. 21. 141 fur. 34 r. 22. 121 m. 6 fur. 1 r. 23. 4629 r. 2| ft. 24. 1 fur. 6 ft. 4 in. 25. 112m. 3 fur. 33 r. 10ft. 26. 2112 steps. 27. 57600. 28. 1 cwt. 2 qrs. 11 Ibs. 29. 3 cwt. 2 qrs. 21 Ibs. 30. 2 qrs. 9 Ibs. 8 oz. 31. 17 Ibs. 32. 3 cwt. 1 qr. 19 Ibs. 2oz. 33. 5 Ibs. 4 oz. 34. 6 Ibs. 3 oz. 11 dwt. 35. 3 Ibs. 1 oz. 2 dwt. 4 gr. 36. 5 sq. ft. 37. 114 sq. yds. 3 sq. ft. 38. 1 sq. yd. 6 sq. ft. 43 sq. in. 39. 12 square rods. 40. 20 square rods, 186 feet. 41. 3 solid yds. 5 s. ft. 42. Ill solid feet, 126 in. 43. 1 solid ft. 605 in. 44. 32 solid yds. 12 ft. 45. 1 solid yd. 565 in. 46. 18 E. E. 2 qrs. 47. 90 qrs. 1 n. 48. 29 yds. 3 n. 49. 83 E. E. 6 in. 50. 373 E. E. 3 qrs. 51. 138 lots, 1 rod over. 52. 459 times, 1J feet over. 53. 31 loads, 18 cwt. over. 54. 177 G. 15s. 55. 60 E. E. 56. 93 balls, 8 Ibs. over. 57. 440 times. 58. 107 kegs, 1 gal. over. SECTION VII. 1. Performed. 2. 22 19s. 8d. 3. 79 12s. 4d. 3 qrs. 4. 230 18s. 5. 2 6s. lid. 6. 121b. 2oz. Odwt. 7 gr. 7. 23 Ib. 3 oz. 10 dwt. 22 gr. 8. 211b.loz. 12 dwt. 22 gr. 9. 25 Ib. 8 oz. 14 dwt. 4 gr. 10. 16 cwt. Oqr. 3 Ib. 10 oz. 10 KEY. 11. 5 T. 12 cwt. 1 qr. 10 Ib. 23. 1 A. 29 p. 63 ft. 78 in. 12. 4 T. 2 cwt. 1 qr. 12 Ib. 24. 1 K. 9 p. 112 ft. 112 in. 3 oz. 25. 8 s. yds. 13 ft. 190 in. 13. 2 T. 10 cwt. 19 Ib. 26. 26 s. yds. 21 ft. 74 in. 14. 5 m. 1 fur. 14 r. 1 ft. 6 in. 27. 101 gals. 2 qts. 15. 105 m. 7 fur. 31 r. 28. 90 bu. 3 pks. 1 qt. 16. 1 fur. 32 r. 2 ft. 6 in. 29. 114 bu. 2 pks. 17. 1 fur. 18 r. 12 ft. 3 in. 30. 36 yds. 2 qrs. 18. 1 m. 34 r. 2 ft. 8 in. 31. 21 d. 6 h. 14 m. 19. 1 m. 6 fur. 10 r. 16 ft. 32. 4 Y. 25 w. 6 d. 20. 32 m. 21 r. 33. 26 deg. 35' 4". 21. 18 A. 23 p. 34. 35 deg. 25' 30". 22. 35 A. 23 p. 35. 95 deg. 27' 22". SECTION VIII. 1. Performed. 15. 1 Y. 14 d. 2. 4 3s. lid. 16. 9 mo. 17 d. 3. 3 8s. 8d. 17. 3 Y. 11 mo. 22 d. 4. 2 bu. 7 qts. 18. 1 Y. 9 mo. 5 d. 5. 23 bu. 2 pks. 5 qts. 19. 1 Y. 9 mo. 22 d. 6. 1 Y. 10 mo. 26 d. 20. 5 mo. 19 d. 7. 8 Y. 9 mo. 3 d. 21. 1 Y. 10 mo. 24 d. 8. 8 gals. 2 qts. 22. 3 Y. 6 mo. 1 d. 9. 13 gals. 2 qts. 1 pt. 23. 2 Y. 9 mo. 7 d. 10. 6 fur. 36 r. 24. 2 deg. 57'. 11. 10 miles, 38 rods. 25. 13 deg. 23'. 12. 1 cwt. 1 qr. 22 Ib. 26. 10 deg. 26'. 13. 2 cwt. 2 qrs. 26 Ib. 27. 9 deg. 16'. 14. 1 Y. 2 mo. 10 d. SE CTION IX. 1. Performed. 6. 117 d. 18 h. 24 sec. 2. 8 11s. 7. 140 bu. 2 pks. 3. 18 12s. 9d. 3 qrs. 8. 187 bu. 1 pk. 2 qts. 4. 1 d. 2 h. 53 m. 9. 96 bu. 2 pks. 2 qts. 5. 2 d. 7 h. 10 m. 6 sec. 10. 3 m. 2 fur. 27 r. 7% ft. KEY. 11 11. 39 m. 6 fur. 13 r. 2 ft. 15. 213 yds. 3 qrs. 3 in. 16. 48 Ib. 6 oz. 15 dwt. 12. 1 T. 1 qr. 17. 87 Ib. 7 oz. 5 dwt. 12 gr. 13. 2 T. 19 cwt 2 qrs. 18. 68 A. 1 R. 33 r. 14. 2 T. 3 qrs. 8 Ib. 19. 216 A. 1 R. 36 r. SECTION X. . 1. Performed. 8. 15 bu. 2 pks. 3 qts. 1 pt. 2. 1 15s. 9d. 9. 9 13s. 4d. 3. 6 4s. 3d. 10. 38 6s. 7d. 4. 6 h. 43 m. 15 sec. 11. 3 Ib. 4 oz. 14 dwt. 6 gr. 5. 9 h. 11 m. 41 sec. 12. 2 T. 10 cwt. 2 qrs. 9 Ib. 6. 14 d. 8 h. 15 m. 3 sec. 13. 1 bu. 2 pks. If qt. 7. 8 bu. 3 pks. 1 qt. 14. 8 A. 3 R. 33J r. SECTION XI. 1. 1 T. 3 cwt. 2 qrs. 14 Ib. 6. 9 m. 20 sec. past 12. 2. 142 8s. 9d. 7. 15 minutes 44 seconds 3. 1 T. 17 cwt. past 7, A. M. 4. 49 m. 52 sec. past 12. 8. 3 m. 56 sec. past 7, A. M. 5. 59 m. 12 sec. past 1. 9. 6m. 28sec. past 11, A.M. SECTION XII. 1. 29, 23. 4. Prime ; 2, 2, 7, 29 ; 7, 2. 2,7,29. 107; 2,2, 3, 3,31; 3. Prime; 19, 19; 2, 7, 53; 3, 2, 41; 2, 2, 2, 1013. Prime ; 2, 2, 79. 5. 2, 7, 19 ; 2, 2, 13, 17 ; 3, 3,3,71; 2,2,2,47. 12 KEY. SECTION XIII. 1. Performed. 13. 1. 14. 2. 15. 2. 2. A. 16. iff 3- f f. 17. if, , if- 4. *. 18. H, *, }. 5. . 19. ||, A, A- 6. Performed. 20. Performed. 7. 437. . 21. Performed. 8. 1, or Prime to each other. 22. 4J, 2^, 3-ft- 9. 1, " " " 23. 7|, 6-&, 2|f. 10. 53. 11. 32. 12. 79. 24. 2f, lllf, 21 A, 18. SECTION XIV. 1. Performed. 20f 93J 29^ 2. Performed. *** 5 ? ~fT, 4 1' Si 22. ^ 129 * 15? * 5. 4,7,5 6. 4. 25^ 34 42| 76j. 7. W- 3 , 4,~5~,~9~. b - ^f 4 -, 97A 78 136J 9. 7 halves. 24 -r 1 -; y* 10 5J. 5 , 4, 7 . 11- 4- 95 H| 46| 74 12. ^a. s , 5,8. 13 ! F ,z F ,i^a. 185M98f }H; 26 - ^r,^r. 16.' If; If, If- 27 144*1104 14 36 52 17 , 13 . 17 ' 26, 56, 60. 28> 141| 162 18. Performed. 7,8. 4 7| i|^ 65^ 81 19 ' -s^'-T. '*-'*- 425 218J Ol/. 4, 5, 6. 20- ^ ^ ^ KEY. 13 SECTION XV. 1. $45. 8. $18f 2. 40t 9. 37^, 3. $52.12. 10. 32^, 48J-, 4. 255f, 105. 11. M cwt. 5. 466f Ibs., 3266 Ibs. 12. 2fV, 2, 2^. 6. 68^ bush. 13. 14J, 115}f, 42H- 7. ^ cwt. ; 130^ cwt. SECTION XVI. 1. 409 bottles. 11. l^V, ?i 2. 31 J loaves. 12. 2f, 3- 2, 4A, fff. . 13. ^ T J T . 4. $876.90. 14. 356, 49^. 5. 11 T 7 T coats. 15. $145.12^. 6. 35J blocks. 16. $196.87|. 7. 3A Ibs., 1173^ Ibs. ' 17. $96.00. 8. 47J, IMl, 9/ T . 18. $42.87J. 9. 414f, 56f, 617. 19. S7911.62J. 10. 25J. SECTION XVII. 1. 2/ T , 1^- 9. 44f bushels. 2. i, J* J. 10. 23^ 3. t, IfH- 11- 4. 2^, l**t 12. 22^, 5- 5^, 7, . 13. 41 A, 6. 106J-J. 14. 7. 80^. 15. 8. $1.03|. 16. 14 KEY. SECTION XVIII. 1. A- 16. . C 2. rir 17- T f*. 3. dk- 18. *% 4. ^. 19. ft. 5. ^. 20. Performed. 6. ^ 21. 8s. lOfd. 7. T ^. 22. 18 h. 40 m. 8. f . 23. 4200 m. 9- WTO WW- 24. 16m. 21ft sec. 10. 4j#. 25. 2 qts. 1 pts. ; 9 gals. 11. IM- i qt. i* pts. 12. ylf^ 26. 10 oz. 16 dwt. 13. ffo. 27. 2 oz. 2 dwt. 8ft grs. 14. /ft. 28. 68^ sq. rods. 15. T ^. 29. 1 sq. ft. 60^f in. SE CTION XIX. I- jiy 12- 2. *TT- 13- 3. |fe. 14. 4. ,4^. 15. 5. ^^T. 16. 6. AVo- 17. 7. rfi*. 18. 8. rfffl* I 9 - 9. iffffS- 20. 10. M|. 21. 11. 4|. SECTION XX. 1. S7.87J. 6. S27.18J. 2. S1.96J. 7. 78 bu. 3. $55.50. 8. $29.25. 4. $27.12|. 9. f cwt. 5. $24.06i. 10. 2J| cwt. KEY. 15 11. 67 cubic feet. 18. S6.95if; $4.54f. 12. 13^ cords. 19. Sll.lO^y; $16.14ff. 13. ,$V. 20. $32.00. 14. ^ of a sq. rod. 21. $1209.60. 15. T i^ of a sq. rod. 22. $2.95^ ; $3.54^. 16. $1.256+. 23. $45.61f$; $30.88 T | ? . 17. 26JJ gals. SE CTION XXI. 1. 201.025. 14. 582.75 ; 3.925. 2. 9683.322. 15. 35.25; 1177.6. 3. 568.1496. 16. 2.226; 15.6. 4. 336.325. 17. .1244; .5583. 5. 3921.065. 18. 262.81 ; 801.325. 6. 159.09 ; 778.73. 19. 22.2882 ; .89. 7. 15.685; 13.143. 20. 44.375; 27.5625. 8. 132.385; 173.41. 21. 7000; 6433. 9. 16.593; 84.16. 22. .11; 248}f 10. 648.079; 255.076. 23. 1708J; 7727^-. 11. 3.776; .4933. 24. 1000; 10000. 12. .684; .5584. 25. .0005; .0032. 13. 10814.1 ; 7816.581. SECTION XXII. 1. .375. T.0487+; .2658+; 2. .625. y - { .9393+. 3. .125; .875. in (.0012+; .0336+; 4. .0625; .1875; .3125. 1U ' "[ .0079+. 5. .5625 ; .6875 ; .9375. 11. Performed. 6. .59375; .71875; .84375. 12. .1^; .18^; 7 (.148+; .2903+; 13. .2105263^. .1470+. 14. .538461538^. .6111+; .1428+; 15. .3809523809^- .0172+. 16 KEY. SECTION XXIII. 1. .2958+. 7. .4646+. 2. .0160416$. 8. .389+. 3. .0198+. 9. .0743+. 4. .09375. 10. .2208+- 5. .3125. 11. .1255+. 6. .2070. 12. .078125. SECTION XXIV. 1. Performed. 12. 112 rods. 2. 4 feet 1.14 inches. 13. 144 rods. 3. 15 feet 6.12 inches. 14. 7 minutes 12 seconds. 4. 4 feet 3.48 inches. 15. 9 minutes. 5. 13 shillings. 16. 2 d. 9 h. 7 m. 12 sec. 6. 16 shillings. 17. 1 d. 3 h. 12 m. 57.6 sec. 7. 8f pence. 18. 50.4 seconds. 8. Iff pence. 19. 97.408 cubic feet, 9. 3s. 9d. 2.4 qrs. 20. 25 solid feet 1036.8 in. 10. 2 pks. 7 qts. 1.36 pts. 21. 94f feet. 11. 3 pks. 4 qts. 1.6 pts. 22. 16Jf feet. SECTION XXV. 1. $7.125. 13. $0.625. 2. $41.205. 14. $0.6975. 3. $49.625. 15. $0.984375. 4. $9.125. 16. $0.584375. 5. $50.52. 17. $71.25. 6. $2.145 loss. 18. $91.875. 7. $8.875. 19. $22.68. 8. $7.45. 20. $121.50. 9. $5.78. 21. $29.75. 10. $4.905. 22. $5.52. 11. $1.05. 23. $0.05. 12. $1.575. 24. 350 Ibs. KEY. 17 25. 26. 27. 28. 29. 30. 12.5 times. 15.5 Ibs. 2625. 1375. 15 barrels. 17.5 barrels. 31. 3 tons. 32. 13.5. 33. 17 tons. 34. 16 times. 35. $3.29. SECTION XXVI. 1. $8.66Jf J gain. 2. $67.08 gain. 3. $23.3 6f gain. 4. $53.02 gain. 5. $16.33| gain. 6. $8.04| gain. 7. $1.68 gain. 8. $9.88 gain. 9. $5.06 gain. 10. $3.23 gain. 11. $15.75 gain. 12. $7.05 gain. 13. $76.01 loss. 14. $1.99 loss. 15. $14.84 gain. 16. $7.70 gain. 17. $23.37^ gain. 18. $10.73 gain. 19. $9.25 gain. 20. $24.45 gain. 21. $2.24 gain. 22. $40.35 gain. 23. $3.00 gain. 24. $0.75 loss. 25. $6.86 gain. SECTION XXVII. 1. Performed. 2. $386.66f. 3. $462.22|. 4. $284.44f. 5. $742.22$. 6. $2311.11$. 7. $374.666. 8. $554.00. 9. $162.111-[-. 10. $319.628+. 11. Performed. 12. 16 14s. 15. 16. 17. 18. 2* 13. 41 18s. 9fd. 14. 126 19s. 6 144 Os. Performed. $506.40. 210 7s. 6d. 19. Performed. 20. $402.083+. 21. Performed. 22. $136.31J. 23. $43.40. 24. $19.83J. 18 KEY. SECTION XXVIII. 1. Performed. 2. S14.0866. 3. $4.0477. 4. $26.8024^. 5. $4.2599^. " 6. $3.604+. 7. $5.496+- 8. $50.912+. 9. $68.142. 10. $36.10. 11. $43.00. 12. $0.626+. 13. $0.445+. 14. $25.666+. 15. $0.327+. 16. $0.47. 17. $2.521+. 18. $1.896. 19. $0.698+. 20. $0.535+. 21. $0.962+. 22. $2.703+. 23. $18.084+. 24. $19.78. 25. $39.56. 26. $26.373+. 27. $23.076+- 28. $16.483+. 29. $75.00. 30. $7.16+. 31. $57.318+. 32. Performed. 33. $2.903--. 34. $2.047+. 35. $0.607+. 36. $4.488+. 37. $0.210+. 38. $584.041. 39. $1039.461+. 40. $501.40. 41. $137.37. 42. $74.829. 43. $567.50. 44. $753.876. 45. $859.575+. 46. $42.201. SECTION XXIX. 1. $143.32. 2. $273.00. 3. $308.887. 4. $565.55. 5. $210.439+. 6. $323.34. 7. $528.011. 8. $112.36. 9. $119.101+. 10. $126.247+. 11. $133.821+- 12. $3.821+. 13. $310.00. 14. $265.00. 15. $280.90. 16. $297.754. 17. $315.619+. 18. $5.619+. KEY. 19 SECTION XXX. 1. S468.367. 6. $496.584. 2. $337.30. 7. $805.845. 3. $921.445. 8. $46.146+. 4. $153.80. 9. $121.339. 5. $310.776. 10. $352.096. SECTION XXXI. 1. $98.95. 2. $443.025. 3. $247.375. 4. $509.34. 5. $593.70. 6. $146.925. 7. $74.587-)-. 8. $989.50. 9. $548.52. 10. $149.175. 11. $100.00. 12. $520.00. 13. $600.00. 14. $10055.30+. SECTION XXXII. 1. 10 per cent. 2. 13Jf per cent. 3. ^ . per cent. 4. $4.816. 5. 2 per cent. 6. $0.316+. 7. $644.061. 8. 6f percent. 9. $5.32. 10. 19| per cent. 11. 43^!^ per cent. ' j.o. ^ufy$t pei uc 14. 151+ per cent. 15. 61+ per cent. 16. 62+ per cent. 17. 10- - per cent. J8. 16-- per cent. 19. 20+ per cent. 20. $300. 21. $88. 22. $20.236+ 23. $15.63. 24. $522.50. 25. $658. 26. $1036.80. 27. $260.25. 28. $622.08. 29. $37.38. 30. 9 A per cent. 20 KEY. 31. $0.51J+- 32. $806.25. 33. $7735. 34. $4.75. 35. $11958.04+. 36. $12000. 37. $781.50. 38. Whole gain, $22.32 ; gain per cent. 34+. 39. Whole gain, $135.02 ; gain per cent. 73-f-. 40. Whole gain, $17.375 ; gain per cent. 41-f-. 41. Whole gain, $393.50 ; gain per cent. 20+. 42. Whole gain, $306; gain per cent. 21+. SECTION XXXIII. 1. $0.649. 2. $0.565. 3. $0.1208. 4. Performed. 5. 3 bu. oats, 1 bu. rye. 6. 1 bu. oats, 1 bu. wheat. 7. 1 bu. oats, 3 bu. wheat. 8. 2 bu. oats, 1 bu. wheat. 9. 35 barley, 7 corn, 14 rye. 10. 13 at 25 cents, 5 at 40 cents, 5 at 33 cents. 11. 15 at 20 cents, 18 at 45 cents, 9 at 54 cents. 12. 1 Ib. at 6 cents, 3 Ibs. at 10 cts., 2 Ibs. at 8 cts. and 1 Ib. at 11 cts. 13. 1 gal. at 60 cts., 2 gals. at 75 cts., 1 gal. water, 7 gals, at 80 cts. 14. 5 bu. at 25 cts., 10 bu. at 30 cts., 10 bu. at 33 cts., 15 bu. at 45 cents, 17 bu. at 50 cents. 15. 24 gals, at $1, 80 gals. at 74 cents. 16. 50 Ibs. at 8 cts., 100 Ibs. at 11 cts., 100 Ibs. at 7 cts., 150 Ibs. at 12 cents. 17. Performed. SECTION XXXIV. 1. Performed. 2. Performed. 3. 2 mo. 16+ days. 4. 6 mo. 6 days. 5. 5 months. 6. 2 mo. 6+ days. 7. 1 mo. 25 days. 8. 3 mo. 10 days. KEY. 21 SECTION XXXV. 1. 225 square rods. 2. 240J square rods. 3. 289 square rods. 4. 30 6 J square rods. 5. 462| square rods. 6. 800 square rods. 7. 1874 square rods. 8. 7191 square rods. 9. 32 rods. 10. 71 acres, 58 rods. 11. 295^ rods. 12. 132|f inches. 13. 3| feet. 14. 16f feet. 15. 4f yards. 16. 34f yards. 17. 3420 feet. 18. $39.33. 19. 1040 rods. 20. 182 dollars. 21. 4 acres. 22. 6 acres 132 rods. 23. 5 acres 33 rods. 24. 20 rods. 25. 36 rods. SECTION XXXVI. 1. Performed. 2. Performed. 3. Performed. 4. 27 ft. V. 5. 45 ft. 11'. 6. 137 ft. 9 / 2". 7. 19 ft. 10'. 8. 15 ft. 7' 5". 9. 127 ft. 11". 10. If cords 14 feet. 11. 5 cords I 1 . 12. 1 cord 1 ft. 13. 106 ft. 5' 9" 4"'. 14. 1 cord 10 ft. 15. 14 cords 3 ft. 16. If cords 7 ft. SECTION XXXVII. 1. Performed. 2. 15. 3. 17. 4. 19. 5. 25. 6. 28. 7. 29. * 8. 31. 9. 125. 10. 246; 324; 462. 11. 1.6. 12. 1.5. 13. 12.5. 14. 3.7. 22 KEY. 15. 100. 16. 1.3. 17. .9. 18. .1. 19. f. 20. | . 21. . 22. H. 23. J. 24. f . 25. .5. 26. 8.366+. 27. 9.486+. 28. 7.745+. 29. 14.142+ 30. 12.64+ 31. 3600 square rods. 32. 9 rods. 33. 39.001+ 34. 17 miles. 35. 33.03+ feet. 36. 21.26+ feet. 37. 26.83+ inches. 38. 23.49 feet. 39. 17.32 feet. 40. 10.39 feet. 41. 6.92 inches. 42. 6.92 inches. SECTION XXXVIII. 1. 5. 2. 6. 3. 8. 4. 9. 5. Performed. 6. 14. 7. 15. 8. 17. 9. 21. 10. 24. 11. 36. 12. 125. 13. 134. 14. 156. 15. 2.5. 16. 3.3. 17. 2.15--. 18. 2.71--. 19. 3.68--. 20. 4.64+ 21. 29.5+ inches. 22. 41.7+ inches. 23. 5.03 feet. SE CTION XXXIX. 1. $8.68. 2. S23.33J. 3. $0.95. 4. 69f miles. 5. 5f dollars. 6. 13/ T cords. 7. 6f months. 8. lOf per cent. 9. 6|f per cent. 10. A, $112.50; B, $67.50. KEY. 23 11. C, $150; D, $90. 30. 12. $187}$; $152-3%. 31. 13. $10f; $9j$. 32. 14. $24|; $12. 33. 15. 19.79 rods. 34. 16. 22.5 acres. 35. 17. 50.84 acres. 36. lft ( Length, 84.84 rods. 37. * 1 Width, 48.08 rods. 38. 19. 2 ft. 9.94+ inches. 39. 20. 116.41 rods. 40. 21. 7.19+ feet. 41. 22. 24.19+ Ibs. 42. 23. 38.41+ Ibs. 43. 24. 2030.56 Ibs. 44. 25. 8.23+ cords. 45. 26. 7.65+ tons. 46. 27. 8315.77+ Ibs. ,- 28. 10823|iJ. 29. 27 hours 8 minutes. 35f days. 2 1 weekg, 47*1 days. Performed ...... - *% ri Y H* V Performed. ours. days. 8|f men. $300. $280; $320. $150 ; $450. $160; $330; $350. SECTION XL. 1. 75. 2. 105; 181; 177; 213. 3. 190; 223; 241. 4. 157; 265; 317. 5. 90; 200; 400. 6. 1 ; 67 ; 571. 7. 17; 197. 8. 45; 169. 9. Performed. 10. 2. 11. 4. 12. 156. 13. 590. 14. 5000. 15. 124800 feet. 16. 168; 14196. 17. 6. 18. 32.2 feet. 19. 257.6 feet. 20. 402.5 feet. 21. 579.6 feet. 22. 7 sec. ; height, 778.9 ft. 23. 8 sec.; height, 1030.4 ft. 24. 144.9 feet. 24 KEY. 1. 4094 2. 1536. 3. $327.68. SE CTION XLI. 4. 5. 32QOOQpOO. SECTION XLII. 1. 113.0976 feet. 2. 3 miles 7 furlongs 1 6 rods 10 feet 6 inches-)-. 3. 76 feet 11 inches. 4. 24899 miles 1 furlong 31 rods 7 inches+. 5. 73 r. 8 ft. 8J- in. 6. 907 r. 15 ft. 2 in. 7. 452 ft. 4J in. 8. 35 r. 7 ft. 3J- in. 9. 35 r. 13ft. ll ? J|^in. 10. The circle is greater by 1.115 rods. SECTION XLIII. 1. 4.714+ cubic feet. 2. 21.2058 cubic feet. 3. 22400 cubic feet. 4. 973.3724 cubic feet. 5. 75.3984 cubic feet. 6. 197343519.161326 m. 7. 1423.672 cubic-inches. 8. 904 feet 1347 inches. SECTION XLIV. 1. 86 and 54. 2. 333 and 239. 3. 115Jan 4. 123^ and 5. 47 and 33. 6. 59 and 41. 7. 85 rods long, 35 rods broad. 8. 156 r. long, 84 r. wide. 9. 53f feet; 36^ feet. 10. 77^ feet; 42} feet. 11. Performed. 12. 6396; 1551; 8096. 13. 1 acre 19 rods. 14. 4 ft. 10 in. 15. 13.1 rods; 5.69 rods. 17. Height, 47.62+ ft; ^ of the whole remained to be built. 18. As2:l; as sq. r.of 2:1; that is, as 1.414+ to 1. 19. 10 miles ; 10 miles ; 14.422+ miles. * KEY. 25 20. 4.97+ inches. Thean- * swer to the 18th ques- tion furnishes the hint for the solution of this. 21. 8 m. 4^ sec. 22. 16h.45m. 5 T \V sec. 23. 14.97+ ft. Regard the stick as the frustrum of a pyramid. See 17th question. 24. 25.525+ acres ; or, 25 acres 2 roods 4 rods. 25. 486 Ibs. 26. 31.82+ Ibs. 27. 5.46+ inches. 28. 6.88+ inches. 29. 254.6+ Ibs. 30. 14.47+ Ibs. 31. 2049 Jibs. 32. 33 ft. 4.256 inches. 33. 18.8+ Ibs. 34. 182f Ibs. 35. 906f Ibs. 36. 2688 Ibs. 37. 448 Ibs. 38. 5^ inches. 39. 9.09+ inches. 40. 3.66+ inches. 41. 23^ Ibs. 42. 60JJlbs. 43. 72* Ibs. 44. 4^ inches. 45. 33 feet. 46. 9.69+ Ibs. 47. 82274.73 Ibs. 48. 7.25+ feet. 49. 2.52+ inches. 50. 94 T 2 F cwt. 51. 60^ T cwt. 52. 75.6617+ cwt. 53. 20.57+ cwt. 54. 39 cwt. 55. 122^ cwt. 56. 84^f cwt. 57. 48ff cwt. 58. 59^ cwt. 59. 20 cwt. 60. 77f jf cwt. 61. 42 cwt. 62. 17f cwt. 63. As 1 to 12. 64. 1728 Ibs. APPENDIX. 1. $351.872+. 2. $265.476+. 3. $397.584. 4. Dec. 22, 1845. 5. $588. 6. $176.50. 7. For himself and oxen, $1.729+ each; for his son, $0.864+. 8. A gained $72.244 ; B re- ceived $4.078 per day ; oxen, $2.719 per day. 3 9. A, 6337 Ibs. 14 oz.; B, 8222 Ibs. 2 oz. 10. $79.703+. 11. $104.50. 12. $29.589. 13. 2.1212+ ; 1.4142+ ft, 14. 50f+ cubic feet. 15. 34.57+ in. ; 21.81+ in. 16. 40 cubic ft.; 630 in. 17. lst,12;*2d,8;3d,30yds. 18. $40. 19. 16 years old. 26 KEY. 20. A'sage,24; B'sage,54. 21. Sift gallons. 22. .416666+. 23. .3015873015. 24. .22916666-)-. 25. 95855760. 26. 1013; 1019. 27. 2 and 11 63. 28 29. Is. 7.13566d. 30. $60.21+. 31. Si 14.1 18+. 32. $630.892. 33. $1244.581+ 34. $460.804+ 35. $137.181+ 36. 3 mo. 11 d. 37. $787.60. 38. $335.447. 39. $684.611+. 40. $222.283+ 41. 607662 sq. in. 42. $25.85. 43. 147 2 sq.ft. 44. $174.37^. 45. 98.706+ 46. 132.02+ 47. 376.85+. 48. 108.526+. , Q ( Width, 10.733 in. iy * 1 Thickness, 5.366 in. , n (Width, 11.384 in. ' I Thickness, 3.794 in. 51. 10 in. long, 10 in. wide, 52. 8.769+. [5 in. thick. 53. 12.01+ 54. 3.1 41+. KK (One gains $179.287. h ( The other, $159.712. 56. 30^. 57. 2811f J. 58. $2218.978 59. 470.016 gallons. 60. 2ft. 11.87+ in. 61. 15 ft. 6.393 in. 62. 12+ per cent. 63. l t V 64. 10^, first term. 65. 3460. 66. TftftV*. 67. l^V, fifth term. 68. $120.38^. 69. $121.659+. 70. 53JHM- 71. W