,M5:r.NRLF ^B 53S M c'C'-^ A COMPLETE KEY TO NEW FEDERAL CALCULATOR, OE IN WHICH THE METHOD OF SOLVING ALL THE QUESTIONS CONTAINED IN THAT WORK IS EXHIBITED AT LARGE. designed to facilitate the labour of teachers, and assist those who have not the advantage of a tutor's aid. BY THOMAS T. SMILEY, TEACHER. Author of an Easy Introdaction to the Study of Geography. Also, of Sacred Geography, for the use of Schools. PiaatrrtjjJxta: PUBLISHED AND FOR SALE BY J. GRIGG, No. 9, NORTH 4th St. AND FOit SALE BY BOOKSELLERS AND COUNTRY MERCHANTS GENERALLY IN THE SOUTHERN AND WESTERN STATES. jo Mpi ^'Vnci-i - Qcil & Mechanical Engineer. aAtf FRANCISCO, GAL. GiFT Eastern District of Pennsylvania, to wU: ********* BE IT REMEMBERED, That on the ninth I T g * day of May, in the forty-ninth year of the Tnde- I * * t pendence of the United States of America, A. D. ********* 1825, John Grigg, of the said district, hath de- Eosited in this office, the title of a book, the right whereof e claims as proprietor, in the words following, to wit : " A Complete Key to Smiley's New Federal Calculator, or Scholar's Assistant; in which the Method of ►Solving all the Questions contained in that Work is exhibited at large. Designed to facilitate the labour of Teachers, and a?^sist those who have not the advantage of a Tutor's aid. By Thomas T. Smiley, Teacher. Author of An Easy Intro- duction to the Study of Geography. Also, of Sacred Geog- raphy, for the use of Schools." In conformity to the act of the Congress of the Unitrd States, entitled, " An Act for the encournj^tMncnt of learn- ing, by securing the copies of maps, charts, and books, to the authors and proprietors of sucii copies, during the times therein mentioned." And also to the Act, entitled, "An Act supplementary to an Act, entitled, ' An Act for tiie encouragement of learning, by securing the copies of maps, cuarts, and books, to the authors and proprietors of such copies, during tlie times tlierein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etchings historical and other prints." D. CALDWELL, C/erA:V ^/le Eastern District of Pennsyhania. Stereotyped by J. ilowc. 3L> nSo CONTENTS. Paffc Simple Addition, - Multiplication, . 7 Subtraction, . 10 Division, . 11 Long Division, - - 13 Compound Addition, - 20 Compound Multiplication, . 26 Compound Subtraction, - 33 Compound Division, - 43 Reduction, . 43 Single Rule of Three, - . 61 Double Rule of Three, - , 69 Practice, - 73 Tare and Tret, - . 87 Interest, - . . 94 Compound Interest, - 100 Insurance, Commission and Brokage, 104 Discount, - lOG Equation, - 109 Barter, - - 110 Loss and Gain, - . 112 Fellowship, . IIG Kxchange, - 119 Vulgar Fractions, . 121 Decimal Fractions, . 127 Position, ■- 132 Involution, or the Raising of Powers, 141 E/olution, or the Extracting of Roots 1 " t7>. Alligation, . 147 Arithmetical Progression, . 149 Geometrical Progression, - 151 Compound Interest by Decimals, 1.52 Annuities at Compound Interest, ir;.3 Annuities in Reversion, . 154 Perpetuities at Compound Interest, ih. Combination, . ih. Permutation, . 155 Duodecimals, - ib. Promiscuous Examples, " * 158 iviS03795 EXPLANATION OF CHARACTERS. Signs. Significations. = • Equal; as 20s. =£1. -f Addition, (or more) as 6-f 2=8. — Subtraction, (or less) as 8 — 2=6. X Multiplication, (or multiplied by) as 6 X 2=12. -^ Division, (or divided by) as 6-f-2=3. : : : : Proportionally ; as 2 : 4 : : 6 : 12. ^J or "^-J Square Root: as ^^64=8. y Cube Root; as ^64=4. A vinculum ; denoting the several quantities over which it is drawn, to be considered jointly as a simple quantity. JOHN S. PI^ELL. QoS & Mechtudcal Engineer, HAJA JfkiLf^CiaCO, A KEY CATi, Etit S-ettt iFeTretal ealculatot^ ~mt9®9*^ SIMPLE ADDITION. EXAMPLES. (8) 4829 1234 6101 3014 5618 (9) 91769 14678 80032 71897 76989 (10) (13) (16) 876994 213678 482906 809769 376980 20796 335365 2760327 (11) 389261 789794 849798 487697 999996 948219 (12) 2136784 8297698 8297694 4897695 1234697 7092032 3769694 4976082 4569761 8213243 4876962 4876920 4464765 31956600 31282662 (14) 37856 975 1234 14 5612 2075 16287 (15) 378269 402607 702 1246 2132 45178 10276 141 5672 82971 34676 1459 427 12 64053 840410 125358 A 2 6 SIMPLE ADDITION. (17) 14 16 23 29 80 31 100 293 (21) 365 807 660 25 37 101 1895 (24) 35 ( 21 66 (18) 36 97 125 384 1176 1818 (19) 3797 9^ 2 75 876 9750 (20) 205 20 340 970 367 1001 3403 14595 (22) 300 75 2 47 33 9784 20150 765091 1075047 (23) tSES. (27) 60 25 125 216 416 75960800 225000 140 76185940 Miles, (28) 37 33 40 35 145 1870529 PRACTICAL EXEBC 25) 275 (26) 30 196 12 5 471 — g47 Sheep, (29) A's 34 B's 47 C's 64 135 (30) 25 15 40 9 89 (31) 8 15 19 12 64 bar. $ (32) 400 for 2000 550 2750 950 $4750 L "*"" "~" MULTIPLICATION. 7 MULTIPLICATION. CASE L EXAMPLES* (8) 3948769768 (9) 87051298 (10) 976201698769 3 4 5 11846309304 348205192 488100849384{^ (11) 456978426976 (12) 8079698769 (13) 97698429769 6 7 8 2741870561856 (14) 28769842369 9 258928581321 (16) 5697698976845 11 '62674688745295 (18) 84976876989 12 56560891388 781587438152 (15) 769829769478 10 7698297694780 (17) 7029876956 12 1019722523868 (20) 4218 (21) 7S21 84358523472 (19) 9021681409671 12 108260176916052 (22) 87692 (23) 95698 4 5 8436 21963 350768 478490 (24) 10691 (25) 31078 (26) 109019 (27) 900078 6 7 8 9 64146 217546 872152 8100702 8 (28) 826870 10 MULTIPLICATION. (29) 278976 11 (30) 12569769 12 8268700 (34) 39786948 197 3068736 150837228 CASE 2. EXAMPLES. (35) 4978829 408 (36) 8735698 570C 278508636 358082532 39786948 39830632 19915316 52414188 61149886 43678490 2031362232 7838028756 49845892788 (38) 49569876 4817 (37) 84016978 3761 (39) 9637842 9078 84016978 504101868 588118846 252050934 346989132 49569876 396559008 198279504 77102736 67464894 86740578 87492329676 315987854258 238778092692 (42) 11271 35 (40) 9786 13 29358 9786 (41) 8475 29 • 76275 16950 56355 33813 127218 245775 394485 '1 (43) 19004 305 MULTIPLICATION. (44) 76976 489 9 (45) 84769 976 95020 57012 692784 615808 307904 608614 693383 762921 5796220 37641264 82734544 (46) 1978987 4809 (47) 49 9807094 6047 17810883 15831896 7915948 68649658 39228376 035470 9516948483 49496403418 1 (48) 37|00 2|00 CASE 3. EXAMPLES. (49) 4870 25|00 (50) 4087 00 906 000 740000 24350 9740 24522 36783 12175000 370282200000 (51) 876956 99 10000 7892604 7892604 868186440000 10 SUBTRACTlOJs. CASE 4. exampj.es. (53) 8976 6 (54) 769G (55) 87698 9 V 9 (56) 20784 12 5,3856 69264 789282 249408 1 8 9 8 9] 430848 62337G ■■■ '^' 6314256 2244072 (57) 81207 11 (58) ^7696 (59) 75687 12 - 7 1 „ , ; . . (60) 34075 6 893277 572352 529809 204450; 12 12 8 e' 10719324 6868224 4238472 1226700' PRACTICAL EXERCISES. (61) ^25 5 (62)15 (63) g250 4 7 (64) gl50i 4\ §125 (65) glOO 25 60 ^1750 {66) 18175 14 Or thus, 100 5 500 500 72700 200 5 g2500 18175 ^2500 254450' .i*»9®d«^ SUBTRACTION. EXAMPLES. (1) 859708 124978 (5) 0076048 (6) 5321478781 7940689 139876956 734790 1135359 392270922 -, ; ^ T-^l DIVISION. 1 1 (7) 100000 84321 (8) 75381478 (9) 102070845 39040217 19768799 15671? 36341261 82302046 (10) 196 ( 37 159 11) 487 (12) 875 (13) 967 (14) 1001 96 302 351 487 391 573 616 514 (15) 9765 1307 8458 (16) 87696 (17) 455692 "* (18) 1000000 10091 300120 1 77605 155572 999999 PRACTICAL EXERCISES. (19) 25 (20) 8 75 (21)7896 (22)4875 (23)1240 375 42 4389 2976 1082 567 ... .— .... .,_ 1 ,^10 17 33 3507 1899 ^158 _ Sum 1082 (24) 5487 2075 3412 325 (25) 25 containing 250 750 9 75 1000 16 175 2075 Sum. .MH«Q9««»- DIVISION. EXAMPLES OF SHORT DIVISION. ,(7) 2)56789^ 28394^ mn (8) 3)3729768769 (9) 4)469769876 ^4 1243256256+1 117442469 , , - , , ^1 12 DIVISION. (10) 6)849768769 (11) 6)756976874 169953753+4 126162812+2 (12) 7)87694213628 (13) 8)80269687 (14) 12527744804 10033710+7 9)376948769 (15) 11)876956788 (16) 41883196+5 79723344+4 12)4976876946782 (17) 12)89769762048769 (18) (21) 414739745565+2 7480813504064+1 2)3976 (19) 3)8769 (20) 4)47876 1088 2923 11969 5)8767 (22) 6)9698 (23) 7)97899 (24) 1753+2 1616 + 2 13985+4 8)80409 (25) 9)981021 (26) 10)897697 10051+1 109002+3 89769+7 (27) 11)9876978 28) 12)4967844 897907+1 413987 PRACTICAL EXERCISES. (29) 2)12 (30) 7)350 (31) 8)8736 (32) 3)3966 6 50 4)1092 1322 273 ■ . ■ LONG DIVISION. LONG DIVISION. EXAMPLES. 13 (35) 13)875(67 78 95 91 (38) 28)1475(52 140 75 56 19 (41) 41)256976(6267 246 109 82 277 246 316 287 29 (36) 15)476(31 45 26 15 IT (37) 18)958(53 90 58 54 (39) 31)4277(137 (40) 37)25757(695 31 222 117 93 247 217 30 335 333 227 222 (42) 48)337979(7041 336 197 192 59 48 11 14 LONG DIVISION. (43) 59)997816(16912 59 (44) 98)999987695(10203956 98 407 199 354 196 538 387 531 294 71 936 59 882 126 549 118 490 8 595 588 7 (45)1 ^25)4697680424(3758144: 375 947 J (46) 396)387690204886(979015668 3564 3129 875 2772 726 3570 625 1018 3564 620 1000 396 180 2244 125 1980 554 2648 600 2376 542 2728 500 424 2376 3526 375 49 3168 358 LONG DIVISION. 1 5 C47) 876)4876020048769(5560232932 (48) 1478)8769820000402(5933576454 4380 7390 4960 13798 4380 13302 ^37 5802 4962 5256 * 4434 5460 5286 5256 4434 2040 8520 1752 7390 2884 11300 2628 • 10346 2568 9540 1752 8868 8167 6724 7884 5912 2836 8120 2628 7390 2089 7302 1752 5912 1390 16 LO^ (49) S7G96)987G97G8720497(112G2 87696 \G DIVISION. 74501 (50)97680 89768214100( 30940 00O0)8976478976|000OC91896 87912 110737 87696 18527 9768 230416 175392 87598 78144 550248 526176 94549 87912 240727 175392 66377 58608 77696 653352 613872 )00(3242 Ans. 394800 350784 440164 438480 168497 87696 80801 (51) 1476980|00000)47 44 3588282 2953960 Rem 6343221 5907920 4353014 2953960 . 1399054 LONG DIVISION .' PRACTICAL EXERCISES. 1 (52) 45)9847(218 90 84 45 (53) 391)1259678(3221 1173 866 782 397 360 847 782 Rem. 37 658 391 Rem. 267 (54) 148)225476(1523 148 (55) 25)375(15 bushels. 25 774 740 125 125 347 296 516 444 Rem. 72 L= B 2 18 LONG DIVISION. || (56) 75)87735840(1169811 75 127 75 (57) 49850)99700(2 99700 523 450 735 675 608 600 * • 84 75 90 75 15 Rem. When the divisor is the exact product of any two ; figures multiplied together. EXAMPLES (61) 5)9756 (62) i 7)l951-fl 1st Rem. ))8491 9)943+4 278+5 2d Rem. X5 25+1=26 104+7x9+4=67 (63) 9)44767 (64) 7)92017 2)4974+1 Rem. 2487 1643+1x7+2=9 1 LO:SG DIVISION. 19 (65) 11)55210 {6G) 6)38751 9)5019+1 8)6458+3 Rem. — Rem. 557+6X11+1=67 807+2x6+3=15 (67) 12)99876 (68) 12)379^7 9)8323 12)3163+11 — — Rem. : Rem. 924+7x12=84 263+7x12+11=95 PRACTICAL EXERCISES. (69) 5)3775 (70) 12)480 (71) 12)14400 5)755 Ans. 151 8)40 Ans. 5 fe 12)1200 Ans. 100 (72) 12)1800 6)150 (73) 12)396 11)33 Ans. 25 Ans. ^3 EXAMPLES IN ADDITION, MULTIPLICATION, SUBTRACTION AND DIVISION. (I) 50 (2) 40 10 (3) 25000 50 20 10 13000 100 2)20 20 2)12000 —25 Ans. 10 g6000 75 Ans. — 20 COMPOUND ADDITION. 1 (4) Bought 8200 Sold 3756 (5) 50)2450(49 mUes. Ans. 5000 4879 200 13200 8635 450 8635 450 Ans. 4565 1 («) Bought 24 bags, containmg 3000 fe Sold 15 1736 Remains 9 bags, containing 1264 ^ (7) Days '365)2920(8 dols. per day. Yearly income 2920 2920 Spends yearly 1769 Savesper year $1151 i.. -^©a*.^ COMPOUND ADDITION. l^'EDERAL MONEY. EXAMPLES. $ ct8, m, $ cts. g cis. (2) 46 79 75 5 (3) 37 68J (4) 72 62- 37 8 95 371 85 87l 43 50 43 25" 20 12| 97 37 5 79 . 56} 45 ISJ 91 37' g267 00 8 g255 87i 42 68| g440 06» COMPOUND ADDITION 21 $ cts. g cts. i ' cU. (5) 54 75 (6) 29 25 (7) 1 182 3^ 371 34 371 2 50 93 18|. 188 68| 871 149 871 603 68| 979 121 2194 181 265 1783 121 18| 1 93J 87o 68| 8579 56| 2 6 87i 372 87- 93i g4012 18J P 0887 06J ^ 1 $ els. $13 25 Ct8, (8) 5 00 (9) 1 871 681 18 60 1 8 87^ 433 1 18| 1 371 14 50 933 871 56J 5 371 87| 37f 3l| 7 20 00 STERLING MONEY. 121 ^82 18| $l_ 683 EXAMPLES. £ s. d. £ *. d. £ *. rf. (2) 7 9 6| (3) 4 6 4 (4) 565 3 7 13. 7 47 19 7 382 13 5 4 5 2 159, 5 3 592 9 2 10 18 lOj 78 6 llj 856 259 17 3 9 8 Ans. 36 1 Ans. 289 18 IJ An 3. 2656 1 3 1 22 <^03irOl ND ADBITIOX. _— £ S. d. £ s. d. £ s. d. (5) 142 16 7 (6) 763 7 4 (7) 69 18 7 489 3 4 39 4 9 175 2 6 726 15 9 162 17 2 1582 19 4 573 4 '8 459 15 175 13 9 628 12 6 473 12 8 143 13 212 8 7 Ans.2560 12 10 Ans. 18^8 16 11 Ans. £ 2359 8 5 £ s. d. s. d. (8) 1776 12 8 (9) 985 4 9 412 16 5 186 13 4 369 7 2 1569 18 4 469 15 10 183 8 573 19 2 ^ 17 4 1987 14 8 7 4823 15 11 Ans. EIGHT 2925 15 Ans. 10414 1 10 POIS WJ AVOIRDU T. cwt. qr. lb. oz, dr. T. cwt. qr. lbs. oz. dr. (2) 7 11 2 16 4 13 (3) 12 16 1 19 15 15 7 3 8 16 7 114 io 2 12 4 13 138 19 1 12 8 13 72 4 2 24 14 3 42 8 3 19 12 4 176 15 . 3 4 15 11 357 6 2 8 3 3 Anp '^'^ft 7 2 6 1 11 Ans. 561 14 1 7 13 8 qr. lb. z.dr. T. cwt. (4) 139 19 3 18 1 13 10 1754 10 2 11 2 14 27 , 3 14 11 13 13 Ans. 1922 6 .2 17 8 8 ^^i;^^,;^;^^ COMPOUND ADDITION. 23 TROY WEIGHT. lbs. oz.dwts.gr. lbs. oz.dwts.gr. lbs.oz.dwts.gr. (2) 185 2 19 20 (3) 16 4 18 6 (4) 172 11 19 22 56 9 15 6 7 9 11 22 12 4 13 12 1472 11 2 17 163 7 12 18 ' 18 5 11 20 385 ^5 / .17 13 ' 119 11 13 18 1 10 Pl ■ 7 I*'* -. -— .. n ^ T^ ., , . ,, , Am 901 ini'i'^^ 010 90 Ann c>i in ft T? 1« APOTHECARIES' WEIGHT. fe 5 3B^r. ife 3 3 9g-r. ft 3 3 B^r. (2) 84 .7 6 12 (3) 18 1 12 (4) 182 3 10 ■ 132 5 2 175 10 5 10 12 10 2 17 16 2 2 2 8 472 3 1 2 3 17 2 4 2 15 1427 6 7 19 11 7 2 10 2 1 19 Id 6 1 9 ■ Ans.667 1 7 2 5Ans.212 5 1 1 11 LONG MEASURE. yd. ft. 171. L. m.f, p. yd. ft. in. L. m. f. p. yd. ft. in. (2) 3 2 11 (3)172 2 3 19 2 2 4 (4)462 17 29 1110 119 000 14 1 3 000110110 20 8 12290010 4 1 2 28 1 2 9 31 10 0040000 000 13 627 00 032 3Ans.46703 140 5 Ans.20 1 1 Ans. 173 1 4 23 210 6 CLOTH MEASURE. E. E, qr, n, E,F. qr, n, (2) 72 3 2 (3) 19 2 3 536 2 1 728 1 2 847 1 3 142 1 1453 2 816 41 2 32 1 2 Ans. 2951 Ans. 1739 24 canrouAD addition , yd. qr. (4) 19 2 14 2 32 3 142 3 na. E. 3 (5) o 1 2 Fr. 143 17 172 182 132 72 qr. na, 3 2 2 1 1 1 3 3 2 1 1 Ans. 210 720 10 A. R. P. (2) 487 2 17 25 3 28 e-V 32 45 1 16 . 26 29 LAND MEASURE. A. r: p. (3) 22 2 700 3^27 47 5 39 47 2 39 3 28 A (4) Ans ( Ai A. R. P. (4) 132 3 25 654 C 17 462 3 25 16 4 1665 3 38 Ans. 652 1 2 Lns. 2931 3 '29 Ans. 858 19 hhd. gal. qt. pt. (2) 385 42 3 1 27 36 2 132 17 729 25 163 47 2 1 Ans. 1438 43 T. h. gnl.qt.pt. 862 10 10 32 1 37 2 32 1 2 1 LIQUID MEASURE. T. h. gal. qt.pt. (3) 19 2 19 45 Oil 3 17 2 21 1 Ans. 65 1 58 863 39 1 DRY MEASURE. B. p. qt.pt (3) 754 2 5 469 2 385 2 7 1 375 1 3 2 B. p. qt.pt. (2) 47 '2 4 1 635 3 247 3 1 285 2 734 2 5 B.p. qt.pt, 4) 144 3 2 1 .0120 3 1 462 3 1 72 5 1 Ans. 1950 7 Ans. 1985 1 1 18. 680 fi COMPOUND ADDITION. 25 TIME. F. m. w?. 6?. h. m. sec. F. m, w, d. h. m. sec. (3) 172 1 4 62 (4) 462 4 5 37 24 34 18 62 11 24 15 4 5 3 27 15 13 Ans 13 21 35 18 6 1 4 13 12 37 187 4 3 2 5 37 28 Ans 524 10 3 3 6 3 25 MOTION, OR CIRCLE MEASURE. | ^g,'> ' '' sig.'> r It sig, « ' '' (2) 2 7 32 16 (3) 5 10 46 38 (4) 45 5 27 24 11 37 18 1 9 18 1 6 17 13 1 47 12 14 21 34 7 38 24 18 2 8 13 54 4 5 42 19 2 52 4 7 12 19 1 15 12 23 11 57 '^Q 47 32 Ans . 8 2 37 36 Ans. 8 10 20 37 Ans. 10 20 22 10 APPLICATION. $ ds. F. qr. na. B,p,qt, fl) 375 45 (2) 57 2 (3) 2 2 142 371 1375 56| 29 3 2 3 3 5 45 1 3 1 1 32 3 38 2 1 2 4 Ans 18f}4 38^ 38 2 Ans. 113 2 A, n Ans. 242 1 3 F. qr, na. P. (4) 142 2 (5) 15 3 32 3 12 18 1 2 108 3 18 Ans. 25 3 2 Ans. 284 30 60 26 COMPOUND MULTIPLICATION. M.fur, p. B. p, qt, (6) 43 3 (7) 756 2 29 34 756 2 57 2 32 756 2 12 3 18 854 6 854 5 Ans. 142 2 4 Ans. 3977 3 2 COMPOUND MULTIPLICATION. EXAMPLES. FEDERAL MONEY. $ ets. g cts. m. $ cLt. (4) 26 18| (5) 100 40 4 (6) 66 18J 6 10 9 Ans. 157 12i Ans. 1004 04 Ans. 505 68J $ da, m. $ ds. (7) 26 37 5 (8) 665 62^ 8 12" Ans. 203 00 Ans. 6787 50 • ENGLISH MONFV. £, s. d, £ s, d. (2) 14 6 OJ (3) 111 11 101 9 lO"' Ans. 128 14 2} Ans. 1115 18 9 COMPOUND MULTIPLICATION. 271 £ 8. d. £ a, d, (4) 37 6 91 (5) 66 ^8 7-J . 6" 9 Ans. 186 13 n\ Ans. 507 17 9| j AVOIRDUPOIS WEIGHT. T.cwt. qr, Ih, oz, dr. qr, lb, oz, dr, (2) 6 14 2 7 5 2 (3) 3 16 7 8 4 10 Ans. 26 18 1 1 4 8 Ans. 35 24 11 CwL qr, lb. (4) 12 6 10 Cwt. qr. lb. (5) 4 3 17 Ana. 15 2 4 ^. TROY \VI U), oz.dwt.gr. lb. (2) 43 8 10 (3) 113 4 Ans. 53 3 19 :IGHT. oz.dwt.gr. lb. oz. dwt. 6 6 (4) 17 9 14 6 10 Ans. 172 1 13 16 Ans. 681 1 12 Ans. 178 1 lbs. oz.dvjt.gr. (5) 41 6 18 2 lbs. oz. dwt. gr. (6) 91 4 14 16 8 Ans. 291 6 14 Ans. 731 1 17 8 APOTHECARIES' WEIGHT. Ik ^ 3 B gr. m ^ Z B gr. (2) 63 10 2 12 (3) 17 5 6 1 4 9 12 Ans. 484 6 7 2 8 Ans. 209 9 4 2 8 1 -n .7--^ . . ^ r—T^, '! 28 (4) Ans. (2) Ans. (4) An. 1 (2) Ans. (5) Ai J (?) 1 COMPOtlSD MULTIPLICATION. Ife339 m ^ Z B gr. 76 4 1 2 .. (5) 95 1 2 1 11 9 11 687 1 7 Ans. 1046 2 3 2 1 11 LONG MEASURE. L, J\l.fur,p. M,fur,p,yd,ft. in, 4 2 2 29 (3) 18 3 20 1 2 10 7 5 33 1 3 3 Ans. 92 1 21 31 2 2 6 40 7 10 M.fur. p. (5) 44 6 20 7 3. 66 48 6 Ans. 31^ 5 20 CLOTH IVIEASURE. iJ.^. qr. na, E,Fl. qr, na, E,Fr, qr. na. 37 4 2 (3) 18 3 (4) 14 1 3 8 12 9 63 1 Ans. 217 4 Ans. 129 3 Yds. qr. na. 19 1 2 5 E. E. qr. (6) 56 3 9 18. "96 3 2 Ans. 609 2 LAND ISIEASURE. l.R.P. A.R.P. A.R.P. A.R.P. 9 3 20 (3) 10 33 ■ (4) 1 3 11 (5) 63 3 18 6 9 10 11 Ans. 119 1 00 Ans. 91. 3 17 Ans. 18 30 Ans. 702 1 38 1 -7^-r— r^ '} COMPOUND MULTIPLICATION. 29 LIQUID MEASURE. T, hhd, £^al. qt, pt. P. hhd. gal, qt, pt. (2) 1 2 16 3 1 (3) 4 1 19 3 1 10 5 ins. 15 2 42 3 (4) T. 3 h. gal. qt. 2 50 2 8 Ans. 29 2 26 Ans. 23 36 1 1 H. gal. qt. pt. (5) 4 41 1 10 Ans. 46 33 1 DRY MEASURE. Bu.pe. qt. pt. Bu. pe. qt. pt. (2) 13 3 2 (3) 110 3 2 4 4 Ans 7 2 (4) B. A4. ^0 qt. pt. 1 7 Ans. 308 3 1 Ans. 443 4 (5) P. 3 qt. 1 9 ns. Bush. 7 1 TIME.- Y. m* w. d. k.min.sec. W. d. h. (2) 17 8 2 6 4 40 18 (3) S 5 22 6 12 Ans. 106 1 2 4 1 48 (4) F. 7 m. w. 4 4 Ans. 63 10 1 1 Ans. 46 1 Y. m. (5) 16 2 w. d. 6 8 A.ns. 121 4 2 6 TT*" 30 (2) Multiply Ans. 1 t (4) 44 COMP(5UN] £ S. d, ^ 37 10 6| 6X a MULT] RULE EXAMPL by 48 :8=48 56 =56 120 =120 Ai 4 .54 PLICATION. 2. ES. % Cts. 7/1. (3) 66 37 5 by 36 6X6=36 225 'f 398 25^0 6 801 r Ans.^2389 50 cts, 25 m. 3 by 7X8= (5) 12 18J by 96 12K8=96 309 77 I 8 146 25 8 Ans. 2478 16 8 Ans. 1170 00 (6) 45 6 d. 9* by 12X10= £ s. d. (7) 96 12 3| by 144 12X12=144 544 1 6 10 1159 7 9 12 Ans. 5440 15 IS. 13912 13 A. (8) 47 R, 3 P. 20 by 5 6X9= (9) 48 7 25 by 88 11X8=88 538 3 35 8 287 1 9 Ans. 2585 1 Ans. 4307 7 COMPOUND MULTIPLICATION 31 I lb. 0) 56 oz 9 .dr. 6 by fi 12X7= 4 84 681 9 7 \n^. 4772 3 RULE 3, EXAMPLES. (2) Multiply 7 Cts. 871 11x4+3- (3] 47 28 cts. 68f 11x6+2=68 86 62^ 4 ■&5k Ans. (5) Ans 315 56» 6 346 23 50 62| 1893 57 371 37| Ans. 370 (4) 49 l^ cts. 75X3 12 1950 75 $ 94 18JX1 10 597 00 941 '? 4179 149 00 25 2825 94 62i 18| Ans. 4328 25 ;. 2919 81J 32 (6) Ans. (8) Ans. (10) Ai COMPOUND MU $ cts, 42 31J-X3 11 LTIPLICA (7) Ans. (9) Ans (") Ans. noN. £ 28 *. d. 7 6iXl 4 465 43J 5 113 10 2 7 2327 126 18| 93J- 794 11 2 28 7 6J 2454 12^ 822 18 81 34 s. d. 8 4|X1 11 Cwt. 7 (^r. lb. 3 22X1 10 378 12 A\ 6 79 1 24 6 2271 34 14 li 8 4| 397 7 1 8 3 22 2306 2 6| 5. 405 1 2 lbs 12 . OS, dwts, 5 8X3 12 Jtf. 4 6 21X3 12 149 4 16 3 67 6 12 7 448 37 2 8 4 4 404 14 4 4 3 23 IS. 483 G 12 418 7 27 (2) Multiply 1 COMlhJUND MULTIPLICATION RULE 4. EXAMPLES, 1 56^X6 (3) 2 10 33 Ct8. 871X6 10 5 65X5 10 28 75X7 10 15 6 30 4 287 50 5 626 00 78 25 9 39 1437 201 17 50 25 25 AUB. 713 64 Ans. 1656 00 (4) 4 cts, 31^X9 10 (5) 18 Ci8. 93JX7 10 43 121X7 10 189 371X5 10^ 431 25 6 1893 75 4 2587 301 38 50 86^ 81| . 7575 946 132 00 871 56| Ans. 2928 18| Ans. 8654 433 34 (6) Ans. (8) Ans 25 CO^irOUND cts. 43JX9 10 MULTIPLICATION. 1 $ Cts. 1 (7) 1JX6 II II 254 371X7 10 171X6 10 2543 75 8 1 75X2 10 20350 1780 228 00 621 03| 17 35 3 1 Ans. 39 £ (9) 37 50 2 00 50 00 10^ 65| s. d. 18 6{X5 10 223'59 56J: 10 cU, 161X9 10 101 65X3 10 379 6 21X7 10 1016 50 9 87S2 12 !• 3 9140 304 91 50 95 481 ^ 11377 2654 189 16 3 16 64 12 7| . 9544 93J 'Ans. 14222 5 3J £ s. d, (10) 48 14 21x9 10" COMPOUND MUIiTirLICATION. 36 487 2 IX 10 4871 10 4 19484 3896 438 3 4 16 8 7 101 Ans. 23819 7 101 (12) £ 8. d, 58 9 6fX6 10 584 15 71x9 lo' 5847 16 3 3 17543 8 9 5263 71 350 17 41 Ans. 23157 6 9 £, s. d, 64 2 8X5 10 641 6 6X 10 6413 6 6 5 32066 13 3206 13 320 13 4 4 4 Ans. 35594 M, /. p. (13) 25 3 18X5 10 254 2 20X6 lb 2543 1 0X2 10 25430 10 5086 2 1525 7 127 1 10 Ans. 32170 4 10 36 F. (14) 48 COMPOUND MTJLTIPLICA in.b.c. Yd. gr.n. 42x7 (15)2221X4 10 10 rioN. Hhd.gal.qt. (16) 4 37 2by 4250 10 45 60 0X5 10 483 10 2X8 10 225 2 2 10 4838 10 2X5 10 2256 10X2 10 459 33 0X2 10 48388 10 2 2 22562 2 3 4595 15 4 96777 24194 3871 338 91 51 1 1 82 , An 67687 2 4512 2 90 10 18380 GOO 919 3 229 48 s. 72290 1 Ans . 19529 48 Ans.125182 02 APPLICATION. gl.07 (3) $5 9 .62J (4) gl.l2l 12 (1) $12.50 (2) Ans. s. d, 2 2 by 7 Ans. 62.50 9.63 Ans. 67.47 6.75 [1 £ (5) 63 (6) 3 -X Ans. 27.00 871 by G 1 8 15 2 9 31 00 8 Ans. 6 16 6 Ans. 248 00 $ (7) 1 COMrOUND MULTIPLICATIOrf, C«*. £ S, d, $ 15^X6 (8) 1 3 (9) 9 10 12 37 ds. 10X5 10 521 10" 15 11 91 0X6 10 15 25 911 Ans. 8 5 910 3 acre X 5 ^ A $ (11) 1 Ans. 10 161 2730 546 45 50 £ (10) s. d. 9 6 per 10 n3.332i 50 ds. 18|X7 10 le cost. 4 15 0X2 10 11 871X1 10" 47 10 3 118 75 2 142 9 2 10 10 . 7 6 237 11 8 50 871 31J Ans. 154 7 6 ins. 257 68| prin IT 38 COMPOUND SUBTKACTIOI^. Again: $\ 37^X7 10 13 75X1 10 137 50 2 275 13 9 00 75 621 g298 g257 g40 37» sold for. 681 prime cost. 68J gain. COMPOUND SUBTRACTION. EXAMPLES. FEDERAL MONEY. g ds.m, ^ cts, $ cts^, (2) From 24 60 7 (3) 60b 62^ (4) 110 ISf Take 19 30 : U^s' 99 10| Ans. 5 30 7 (5) $ ds, m. 960 10 2 9 Ins . 960 09 3 Ans. 5 $ 449 1 98 87^ (6) ds. 621 06| Ans. 448 55J Ans. 11 81 $ ds. (7) 1866 00 Ans. 1587 88| COMPOUND SUBTRACTION. $ ds. $ els, m. (8) 104 06* (9) 4010 14 4 (1 9J 1011 12 5 0) ns. 7 8 $ 400 211 3d cts, 00 121 Ans. 103 961 Ans. 2999 1 9 A 188 d, 6 H 871 ENGLISH MONEY. £ s. d, £ (2) 47 6 7| (3) 419 28 5 101 227 Ans. 19 9J Ans. 191 18 8f £ s. d, (4) 1000 11 113 200 9 £ (5) 1000 60 s, 2 7 d. 51 Ans. 800 2 11| Ans. 939 14 n AVOIRDUPOIS VVEIOHT. T, cwt. qr, lb, oz, dr, cwt, (2) 18 16 1 16 9 2 (3) 9 19 3 20 6 qr, lb. oz 3 20 2 2 23 5 Ans. 17 16 1 24 8 12 Ans. 9 24 13 T, cwt, qr, lb, (4) 14 10 2 16 n ^g^^ Cwt (5) 400 . qr 3 .lb. 14 Ans. 14 10 2 5^^^^ Ans. 397 14 TROY WEIGHT. lb. oz, dwt.gr, lb. oz. (2) 8 3 2 (3) 106 2 1 18 6 10 6 dwi 2 15 20 Ans. 6 1 1 20 Ans. 95 5 17 19 40 COMPOUND SUBTRACTION. lb. oz.dwt,<^r. 11). oz.dwt.gr, (4) 22 12 ^6 (3) 16 14 6 110 12 11 10 11 Ans. 7 6 16 Ans. 3 9 13 APOTHECARIES' WEIGHT. Ife339^. fe53 ife33 (2) 48 9 6 1 4 (3) 59 1 2 (4) 69 1 10 2 8 63 7 5 14 9 1 Ans. 46 11 5 1 16 Ans. 5 5 5 Ans. 54 2 7 CLOTH IVIEASURE. yd. qr.nci. yd.qr.na. E.E.qr.na. E.F.qr. (2) 950 12 (3) 49 2 (4) 66 4 (5) 44 1 19 2 3 16 2 1 17 2 19 2 Ans. 930 2 3 Ans. 32 2 1 Ans. 49 3 2 Ans. 24 2 E.Fl. qr. Yd. qr. na. Yd. qr. na, (6) 963 1 (7) Bought 17 2 (0) 75 3 1 174 2 Damarred 2 3 1 1 Ans. 788 2 Remains good 14 2 3 Ans. 75 3 LpNG MEASURE. Dcs:;. m . fur. p. M.fur. p. (2) 20 50 4 20 (3) Travels first day 43 5 20 11 56 30 second do"^. 32 4 00 Ans. 8 54 3 30 Ans. 11 1 20 more. LAND MEASURE. A. R. P. A. R. P. (2) 502 2 10 (3) 69 1 ^3 111 3 9 17 3 2 Ans. 390 3 1 Ans. 51 2 1 m COMPOUND SUBTRACTION. ^ LIQUID MEASURE. T, khd. gaL qt. pL Hhd, gal, 100 -1 19 ^ 1 (3) 2 99 1 28 3 1 29 41 Ans. 3 Ans. 1 34 (4) From I pipe of wine, which is 126 ffals., subtract 93, leaves 33 gals, of wine. Then from 4 nhds. of brandy, subtract 29 gals., leaves 223 of brandy. Then from2 bbls. of beer, subtract 1, leaves 1 barrel, which is 31i gals. Answer, 33 gals, wine, 223 gals, brandy, 31^ gals. beer. DRY MEASURE J5. p. qLpt. B. p. qUpL B. p. qt.pt. (2) 10 I (3) 695 3 1 (5) 600 2 7 1 9 2 6 1 589 3 5 146 3 2 1 Ans. 12 Ans. 105 3 3 1 Ans. 453 3 5 TIME. H. min, sec. (2) 16 29 33 7 36 44 Y. m. Wr (3) 18 11 2 9 10 3 Ans. 8 52 49 F. m. IV. d, (4) 900 111 6 2 6 (5) Ans. 788 6 1 1 Ans. 9 3 y. m. 6 1 1 1 d. h. 1 1 s. 4 10 2 5 23 MOTION, OR CIRCLE MEASURE. sig. ^ ' " sig. "^ ' " sig, ** ' " (2) 9 7 40 8 (3) 10 10 16 12 (4) 11' 2 5 14 7 9 57 19 7 24 37 59 ; .907 20 Ans. 1 27 42 49 Ans. 2 15 38 13 Ans. 2 1 52 $A T>% APPLICATI(»r. (1) 6 feet of chain at $2,75 per foot = $16 59 A gold ring for 4 50 Ear-rings 12 00 42 COMPOUND SITBTR ACTION. g33 00 whole amount. Ring 4 50 has been returned. To receive $28 50 (2) 2 doz. pairs at 75 cts. 16 yds. at 87| — 28 do. at 22 — 5 pair at 31 J — Amount Note delivered Must be returned A, R, P. (.3) 1 St tract contains 690 2 16 2d do. do. 400 3d do. do. 63 3 21 4th do. do. 63 3 24 $ cts. :7= 18, 00 =r= 14 00 rrr 6 16 1 56J 39 50 72| 00 10 27J £ s. d. (4) 55 6 7 41 4 6 75 Collected 171 11 1 In the whole 1218 1 24 Lost 40 6 Sold 200 00 I have 131 5 1 Remains 1018 1 24 Bu,p. (5) Bought 400 3 of wheat, Sold 225 1 do. Remaining 175 2 Bu. p. Bit. p. 160 Oof rye, 150 2 of oats, 37 2 do. 78 3 do. 122 2 71 3 COMPOUND DIVISION. 43 COMPOUND DIVISION. EXAMPLES. $ cls, $ ' cts, $ ch. (3) 3)366 18 J (4) 6)384 S^ (5) 8)496 75 Ans. 64 141-f 2 Ans. 62 09|-f 4 tf cts* ^ cts* ^ cts, (6) 9)587 68J (7) 11)976 43J (8) 12)1979 331 Ang. 65 293-f 4 Ans. 88 76^-f 9 Ans. 164 94-J-f 4 £ s. d. £ s, d. (9) 3)560 9 7 (10) 5)475 19 •9J Ans. 186 16 6J-f 1 Ans. 05 3 ll^J-fl £ ,9. d, £ s. d, (11) 8)596 15 61 (12) 12)756 4 llj Ans. 74 11 ll|-f2 Cwt, qr, lb, , ' Cwf, qr, lb. Yds. qr. nn, (13)5)45 3' 27 (14) 9)10 \b (13) 7)44 J 2 ■ Ans. 9 22+1 Ans. 1 14-f-l Ans. 6 1 l-f3 Yds, qr, na. M. fur, p, JSl. fur, p, (16)11)56 3 3 (17) 12)105 5 22 (18) 6)45' 7 18 Ans. 5 2-f9 Ans. 8 6 18+6 Ans. 7 5 9+4 When the divisor exceeds 12, but is the exact product of any two figures in the multiplication table. $cts.m. $cts,m. (19)6 )45 66 5 ;(20) 4)98 77 8 6l7]r0+5 ^^^ 11)5^+2 ^^^^ Ans. 126 8+2x0+5=17 Ans. 2 24 4+10x4+2=42 44 COMPOUND DIVISION. ^cis.m, $ cts, (21)12)77 87 5 (22) 12)288 68| 8)6 48 9+7 9)24 05l-fl Rem. Rem. Ans. 81 l+lXl2+7=19An».2 67|-f lXl2-f 1=13 ds. m. (23) 12)^6 37 5 11)41 36 4+7 Ans. 3 76 0+4x12+7=55 Rem. £ s. d. (24) 4)87 19 44 8)21 19 10+2 Ans. 2 14 11 + 6x4+2=2/ qrs.r=:J+2 Rem. £ s. d. £ 8, d. (25)3)55 4'7| (26)8)97 15 6} 7)18 8 21+1 7)12 4 5}+l . 1 Rem. ; Rem. Ans. 2 12 7+6x3+1=19 Ans. 1 14 11+1x8+1=9 H}id.gal. qt. JThi.gaX. qU (27)7)44 28 2 (28) 12)150 47 3 9)622042 10)12351+11 Rem. Rem. Ans. 0441 + 7X7+2=51 Ans. 1 160 + 5x12+11=71 COMPOUND DIVISION. 45 When the divisor exceeds 12, and is not the product of any two figures in the multiplication table. ^ cts. ^ cts, m, (31)78)196 75(2 52 2 An 3. 156 $ cts, $cts,m, (32) 97)496 871(5 12 2 485 78)4075(52 cts. 3900 97)1187(12 cts. 97 175 217 156 ' 194 78)190(2 mills. 156 23 10 Rem. 34 97)235(2 mills. ] 194 41 Rem. g cts, $Ct9, (38)123)376 811(3 06| An? 369 £ s, d,£ s. d. .(34)87)44 7 6(0 10 2\ Ans. 20 123)781(6 cts. 738 87)887(10 shillings. 87 43 17 4 12 123)172(1 123 87)210(2 pence. 174 49 Rem. 36 4 S7)144(1 farthing. 87 57 Rem. 46 COMPOUND DIVISION. £ », d,£ f. d. (35) 148)156 15 8|(1 1 2J nearly, Ans. 148 8 20 148)175(1 shilling. 148 27 12 148)382(2 pence. 296 36 4 147 148 PRACTICAL EXAMPLEg, $ ds. «»• i! dt, t di. (1) 6)47 87 5 • (2) 112)64 81}(o 57j Ans. || - 100 *P_ 97 9+1 - 112)6481(57 ct«» Ans. 1 99 4-f3x6-f.l=:l^Eem. 560 881 784 97 4 U2)389(S 336 43 Rem. C03tP0Uril> DIVIBION. 47 (3) 72)56 25(0 78 1 An&. 100 $ cts.$ct8.m. (4) 63)125 00(1 98 4 Ans. 63 72)5625(78 Ct8» 63)6200(98 cts. 504 567 685 530 576 504 9 26 10 10 72)90(1 mill. 63)260(4 miUs 72 252 18 Rem. 8 Rem. £ s. d. (5) 4)18 17 6 Ans. 4 14 4| £ s. d, £ s. 7500thir(ls. Ans. 110000 qrs. Ans. 100 dimes. (tl) 220 10 ' 2200 dimes. 10 22000 cts. 10 Ans. 220000 mills. JSTote. — When more than one denomination is given to be reduced. $ cts, $ cts, $ cts, (1) 15 15 (2) 2 25 (3) 17 18f 100 100 100 Ans. 1515 cts. 225 cts. 1718 cts. 4 4 Ans. 900 4ths. Ans. 6875 4tlis. 50 REDUCTION. $ cts. (4) 13 27,J 100 % Ct8, (5) 426 881 100 1327 3 42688 2 Ans. 3982 thifds. Ans. 85377 halves. ENGLISH MONEY. £ 364 20 70 12 (5) 12 4 (2) 364 (3) 20 (4) 20 12 Ans. 7280 s. Ans. 240 df. Ans. 840 d. Ans. 48 qrs. d. £ s,d. £ s, d, £ 8. d. (6) 26 (8) 18 12 7 (9) 105 13 91 (10) 36 19 7J Ans. 104 qrs. 20 372 12 Ans. 4471 (/. 20 2113 12 25365 4 20 739 12 8875 4 Ans. 101462 Ans. 35503 qrs. Cents to Pence. (2) cts, 36975 9 (3) 57697 9 10)332775 Ans. 332771 (f. 10)519273 Ans. 51927|-f£?. EEDUCTION. 51 (2) 4590 10 Fence to Cent^, d, (3) 76975 ^0 9)45900 9)769750 Ans. blOQds, AVOl Cwt, (2) 260 (3) 4 Ans. 85527^5. 1 m,+l RDUPOIS WEIGHT. qr, lb, oz, 36 (4) 17 (5) 20 28 16 16 Aas. 1040 qrs. Ans. 288 102 . 120 72 17 20 1008/6*. Ans. 272o5r. Ans.320rfr. T, cwt, qr, (6) 5 12 2 20 Qr. lb, oz, (7) 2 25 10 28 112 4 21 6 Ans. 450 qrs. 81 lbs. 16 486 82 1306 ounces. 16 7836 1306 Ana. 20896 drams. 52 KEDXTCTION. APOTHECARIES* WEIGHT. 3 (2) 72 8 ft f^ i 3 Bgr. (3) 10 (4) 15 9 4 2 17 12 12 Ans. 576 drams. 120 ozs. 8 189 oz. 8 960 drs. 3 1516 drs. 3 2880 scru. 20 4550 scni. 20 Ans. 57600 grs. Ans. 91017 grs. CLOTH MEASURE. | Yds. (2) 36 4 E.E. (3) 20 5 E.Fl. (4) 16 3 Ans. 144 qrs. Ans. 100 qrs. 48 qrs. 4 Ans. 192 na. E.FL qrs. (5) 5 2 3 E.Fr. qr. (6) 37 2 5 Yds. qrs. na. (7) 19 2 1 4 Ans. 17 qrs. Ans. 187 qrs. 78 4 Ans. 313 na. KEDUCTION. 53 DRY MEASURE. Pe. Bu, Bu. m 32 8 (3) 7 4 (4) 12 4 Ans. 256 qts. Ans. 28 pe. 48 8 384 2 Ans. 768 pts. (5) Bu, pe, 14 4 56 8 qt, 3 (6) Bu* pe, qt, pt, 24 1 2 1 4 97 8 Ans. 451 qts. 778 2 Ans. 1551 pts. LAND MEASURE. A. ^. 12. P. (2) 132 4 528 .(3) 54 3 23 4 219 Ans. 40 Ans. 40 8783 21120 p. fe^-~ 54 REDUCTION. SQUARE MEASURE. Sq, yds. Sq.yds. s,ft. s.in. I (2) 120 (3) 29 2 102 1 9 9 1080 263 144 144 4320 1054 4320 1052 Ans 1080 264 . 155520 sq,in. Ans. 37^74 sq, in. LIQUID ]VIEASURE. Gals. Hhds Gals. Tims. (2) 28 (3) 5 (4) 110 (5) 6 4 63 4 4 Ans. \\2qfs. Ans. 315^a7s. 440 24 ^ 63 Ans. 880 p/5. 72 144 Wids. gals. qts. Gals. qts. (6) 7 41 2 (7) 47 2 1512 63 4 4 22 190 6048 46 2 2 482 Ans. 380^^5. Ans. 12096 |)f« 4 Ans. 1930 qts. ' REDUCTION. 55 Hhs. gals. qts. Tvnskhds.gals. Tun.hhd.gal.qt.pt. (8) 4 3 (9) 19 27 (10) 5 1 15 1 1 63 4 4 252 4 76 hhds. 21 63 63 1011 2 235 68 458 127 Us. 2022 pts. 4815 1338 4 4 Ans. 19260 (?f.9. 5353 2 Ans. 10707 ;?f*. LONG MEASURE. Yds, (2) 48 3 (3) Po. Fur. Miles* 27 (4) 18 (5) 34 b\ 40 8 Ans. 144/^ 135 Ans. 720|>o. Ans.272/wr. 131 _ Ans. 1481 yds. L. M. M. (6) 108 ^ (7) 17 (8) 20 3 320 p.~l on. 1760 yds,=l m. Ans. 324 vi. 340 Ans. 35200 yds. — « 51 Ans. 5440^0. 56 BEDUCTION. X. FL in. Yds. ft. (9) 6 3 (10) 14 9 12 (11) 37 1 3 18 Ans. 177 m. Ans. 112/jf. 8 Fur, po. 144 40 (12) 112 29 40 5760 ^)4509 ^ 28800 22545 2880 2254^ Ans. 247991 yds. 31680 3 L, m.fur (14) 2 1 3 .po. yds. ft. in. 16 3 2 10 95040 Ans. 12 n. 3 7 1140480 i 8 59 40 (13) Ans. M. fur, 450 6 8 po. 32 3606 40 1)2376 144212 po. 11883 1188 13071 ^ 3 39215 Ai 12 IS. 470590 in. REDUCTION. 57 TROY WEIGHT (2) 116 20 lb. oz. dwt. (3) 25 (4) 29 16 12 20 lb.oz.dwt.gr. (5) 19 11 14 21 12 Ans. 2320 dwt. 300 Ans. 596 dwt. 20 239 20 Ans. 6000 24 4794 '24 24000 12000 19177 9590 144000 g-^-. Ans. 115077 ^r. TIME. (1) 30 60 hrs. 60 yrs. (3) 12 12 Ans. 1600 s. Ans. 720 w. Ans. 144 m. (4) d. kr> min. 3 5 29 24 17 6 77 60 Ans. 4649 -min. 68 EEDUCTION. MOTION, OR CIRCLE MEASURE. (1) 24 (2) 4* (3) 11*12 (4)4 3 18 27 60 30 30 30 Ans. 1440 ' 120 Ans. 342 123 60 60 7200 7398 60 60 Ans. 432000 Ans. 443907" PROMISCUOUS EXAMPLES. ^ Fur, Days. H.cls. (1) 35 (2) 8)98 (3) 7)365 (4) 2)84 100 — — Ans. 12 m. 2/i/r. Ans. 52 1/?. 1 d, Ans. 42 cts. Ans. 3600 cts, — — — TunscwU R, S, P. (5) 8 15 (6) 63 (7) 2I0)15|7 (8) 4)175 20 40 , Ans. £7 17*. Ans. 43 6«. Sjjc. Ans.l75ctt?f. Ans.2520 59. 2>cr. — cts, Pts, Sec, Hhd.gcd, (9) 100)76|42 (10)2)103 (11) 6|0)72|0 (12)733 Ans. J576 42 c^. Ans. 51 qts, Ipt, Ans. 12 mm. — 45 Ans. 474 gal. REDUCTION. 69 Qrs. Dwis, S. (13) 5)100 (14) 210)10|8 (15) 2|0)25|0 Ans. 20 E. E. Ans. 5 oz. 8 dwt Ans. £12 10*. 3 s,d. Days, Qrs, (16) 7 (17) 8 8 (18) 7)203 (19) 16 3 12 4 — Ans. 29 w. — Ans. 21 9 Ans. 104 d?. — ' Ans. 64 im, drs, S, Thins, (20) 16)74(4oz.l0 : : 7 : 276 For 8832 X 7=61824 which -^ 224=276 yds. Ans. Ih. cwt. qrs. lbs. cts. ^ cts. m, (29) As 1 : 5 2 17 ; : 91 : 60 13 5 lb. lbs. cts. § cts. in. Or, as 1 : 633 : : 91 : 60 13 5 For9lX 633=6013^ which -Hl=^60 13c^5.57n. Ans. its. jJ lb. Ibs.fiz. dr. (30) As 114 : 354 : : 1 : 310 8 6+84 For 1X35400=35400 which -M 14=310/6*. 8 or. 6 Jr. + 84 Ans. £, s. £, s. skeins, skcms. (31) As 2 10 : 105 3 : : 100 : 4206 s. s. skeins, skeins. Or, as 50 : 2103 : : 100 : 4206 For 100X2103=210300 which -r 50=4206 sk. Aus. yds. yd. ' ^ cts. j^ cts. m. (32) As 39 : 1 : : 350 38 : 8 08 4+ Ans. For 35038 X 1=35038 which -r39=,^8 ^cts.Am. SINGLE RULE OP THREE. 65 get Is, qts, gals. qt. pt. gals. qi8. pt. (33) ei^gah.^Ql 2+62 1 1 = 123 3 1 pL gals, qts.pt. ds. ^ cts. Then as 1 : 123 3 1 : : 37| : 371 62i pt. pis. cts. ^ cfe. Or, as 1 : 991 :: 37i : 371 62^ For37iX 991=^371621 which -rl^^3716?id*.Ans. bu. bu. hu, ^34) 75+87=162 hu. hu. cts. fi cts. Then as 1 : 162 : : 52 : B4 24 For 52X162=8424 which -r 1=^84 24 ds. Ans. (35) 1 year equals 365 days. day. days. cts. ^ cts. Then as 1 : 365 : : 1871 : 684 37X For 187^X365=384371 'which +1=^684 37| d*. the sum he spends in a year ; his income yearly is ^1022—^684 37| c^.=|337 621 ds. Ans. cwt. cwt.qrs. lb. ^ cts. ^ cts. (36) As 1 : 4 3 24 : : 2 10 : 10 42| lbs. lbs. cts. ^ cts. Or, as 112 ; 556 : : 210 : 10 421 price of stove. For 210X556=110760 which ~n2=JlO 42^ cts. price of stove. Then 27 Ws. X 18j c/^.=g5 06 j- cts. amount of pipe, and 50 c^A'.x2=gl.OO nrice of 2 elbowi5. + ^10 421 ctv, price of stove. 4-^ ^ 06}- cts. do. pipe- -fg 1 00 c^. do. elbows, $16 48 J Ans. (37) 14 pair X 2=28 single shutters, which X 8^=243 whole number of sheets used. sheet sheets, cts. $ cts. Then as 1 : 243 : . Ill : 27 37 For 243X 11^=2737 which +1=^27 37 cts. Ans. -—-/ [ ■ ■ ■ J I -J ■ I • ! 6G SINGLE RULE OF THREE. (38) If 45 men eat 1 lb. per day each, they will alto- gether eat 45 lbs. in a day. lbs, lbs» (1. w, d. Then as 45 : 45G0 : : 1 : 14 2 For 1X4500=4500 which -^45=^100 d,^\ 4 ^veeJi's 2 days, Ans. A.R, A.R,P, hu.pe, hu, pe,qts,pt. (39) As 12 2 ; 37 3 5 : : 443 3 : 1341 7 1 P. P. pe, hu, jte. qlft, pL Or, as 2000 : 6045 : : 1775 : 1341 7 1 For 1775x6045=10729875 which -^2000=1341 hu. pc, 7 qts, 1 pt, Ans. $ ds, (40) Amount paid for the sugar 204 00 carriage 15 75 storage IB 31} and would fjain 57 00 g295 00} the sum the whole must sell for. Cqrs, C, $ cts, $ cf.s,m. Then as 27 2 : 1 : : 205 0G| : 10 72 9-fCO qrs» qrs, cts. $ cts.vi. Or, as 110 : 4 : : 29506} : 10 72 9-f 60 For 29506}X 4=118025 which —110=^10 '72 cis. 9 7«.-f60 Ans. (41) To find how much per cent, he can ijay. $ cts, $ cts, $ % As 18284 40 : 9142 20 : : 100 : 50 per cent. For 100x914220=91422000 which -M828440= 50 Ans. the first. To find what the creditor is to receive. $ cts. $ cts. $ $ As 18284 40 : 9142 20 : : 472 ': 236 For 472X914220=431511840 which —182^440= p2e Ans. SINGLE RULE OF THREE. iSJ INXmSE PROPORTION. m. VI. . d. d. (42) As 12 : 6 :: 18 : 9 For I8x 6r=l08 wlxich -f- 12=9 days. Ans. m. Tiu d, dk h, (43) As 18 ; 12 :: 20 : 13 4 For 20 X 1 2=240 which -^18=13 days 4 hours. Ans. d, d, m, m. (44) As 4 : 24 : : 8 : 48 For 8 X 24= 1 92 which -r 8=48 men, Ans. nu m. d. d. (45) As 48 : 12 : : 24 : 6 For 24X 12=288 which —43=6 days. Ans. h. h. d. (/. k. (46) As 15 : 11 : : 5 : 3 8 For 5X 11=55 which -rl5=3 days 10 hmirs. Ans. ft. in. ft. in. ft. yds. ft. in. (47) As 2 3 : 30 6 : : 48 : 216 2 8 in. in. ft. yds. ft. in. Or, as 27 : 366 : : 48 : 216 2 8 For 48X366=17568 which —27=650^4/^=216 yds. 2ft. 8 in. Ans. d. d. > m. m. (48) As 50 : 100 : : 14 : 28 For 14X100=1400 which -f-50=28 men. Ans. PROMISCUOUS EXAMPLES. Cwt. Cict. qrs. lbs. ^ ds. (49) As 1 : 18 3 19 :: 11 371 Cict. qrs. lbs. lbs. For 18 3 19=2119 which X 1137i=24l0362Jlthe divisor; which —1 ctc^., that i3"'ll2 ;6^.=|215 21-5^ ds. Ans. ^ $■ $ (50) 730—22=708 yds. yd. $ $ds.m. Then as 156 : 1 : : 708 : 4 53 8-f- Ans. For 708X 1=708 which ~-156=g4 53 ds. 8 m.-f 72 GO Sl.^GtK RULE or THREE. (51) To find the prime cost. C, C. qrs. lbs. ^ ttx. ^ cts.m.. 1 : 19 2 17 : : 9 31} : 183 00 7-f- ' lbs. lbs. ^ els. ^ cts. m. Or, as 112 : 2201 : : 9 31| : 1B3 00 7+ For 93lAx2201=:20496Gl| which -M12=gl83 00 cts. 7 m. 4- Alls. To find the sum it sold for. lbs. lbs. g cts. % cls.m. As 112 ; 2201 : : 10 65 : 209 29 1+ For 1065X2201=2344065 which ~112~: C^*. 1 m. Ans. To find the gain. It sold for ^209 29 cts. 1 »i.— Jl83 00 cts. 7 m.rz:g26 28 cts. 4 m. yds. yd. ^ cts. cts.m. (52) As 47 : 1 : : 14 75 : 31 3-f For 1475 X 1=1475 which -^47=31 cts. 3 m.+ Ans. (53) 3 qrs. wide : 1| wide : : 3 J long : 61 long. For 3|=15 ^r*. and ^\^=:b qrs. therefore 15X5= 75 which —3=25 ^rA'.=the quantity of hoUand requisite for each suit, and this ib qrs.x'^^^ suits or men=8850 qrs. which —4=22121 yds, Ans. (54) First ^Sft. : 250 ft. : : 33^1;. 10 m. : 338/?. 4 in. For 33 10X12=406 in. X250=101500 which -f-2c =4060m.=338/if. 4in. the length of the shadow of the tower. Then as the shadow is 1 Sft. 6 in. longer than the width of the river, consequently 338/1?. 4 m.— 18/if. 6 m.=319^. 10 in. the width of the river. Ans. (55) First, 24 hrs, : 1 m. : : 360 deg. :17 m. 2 fur. 1st Ans. For 360X691X1=25020 and 24 Ar5.x60=1440; therefore 25020-f-1440=17 m. 3 fur. Again, 24 hrs. : 1 m. ; : 360 deg. :11m. 4/ttr.= the velocity of the earth in lat. 40 deg. For 360X46=16560-M 440=11 m. 4 fur. Then, 1 7 m. 3/i^r.— 1 1 m. 4/wr.=5 m. Ifur. 2d Ans. DOUBLE JlVhE OF THRKE. (j9 DOUBLE UUI.R OF THREE. EXAMI'J.ES. (2) Thus 3^. • ^8 ^.. ) ^^^^^ ^ l70A,2R.2GP,20yd8.+ For 8X24X32=61 14 the dividend. And 3 X 1 2=36 the divisor. Then 6144-7-36=170.3. 2 R, 26 P. 207jds,-\- Ans. (3) Thus lOox. : 20ox, > ^ /, ^ ^ ^ ^ 18./. .27.7. r' ' ' For 20X27X2=1080 the dividend. And 18X10=180 the divisor. Then 1080-7-180=6 .'I. Ans. W^^^^%^;^-]:: 36/6.. : 48 /&.. . For 24X5X36=4320 the dividend. ' And 9 X 10=90 the divirior. Then 4320-r90=48 lbs. Ans. (5) Thus $100 : SJS335 ? . . ^g . ^30 15,^, For 33r> X 18 X 6=361 80 the dividend. And 100 X 12=1200 the divisor. Then 36 180-M 200=^30 15 ds. Anc. (6) Thus 20m. • 46m.K. ^.^ 3^,^^^^ ^ g^^g g, ^^^^ For 46X32X5631]=8289200 the dividend. • And 20X5:;= 100 the diviBur. Then 8289200^ 100=g828 92 cf*. Ans. (7) Thus n-m. : 12?7i. > ...^ . r.A ' • 30./. : 90ri. l'-'' ^^20prm'..: 540;>air.. For 12X90X120=129600 the dividend. And 8 X 30=240 the divisor. Then 1 29600—240=540 paiW. Ang. (8) Thus 12p. : 38/>. ) ^^„ ..^ „ ,-0 4//. : 16r/. \ ' * ^^^^^^- ' '^^^ ^^'' ^^^''''' For 38X16X37=22406 the dividend. And 1 2 X 4=48 t lie divisor.* Then 22496-MJ;r^-. 168 lbs, lOJor. Ans. 70 DOUBLE RULE OP THREE. (9) Thus8/fc. : 12/i. > .' . to Wo _l For 12x7x5—420 the dividend. And 8 X 4—32 the divisor. Then 420-^32=134- Ans.# (10) Thus liyds, : 247jds,2qrs. > : : gl7 37-J c^. : ,^132 3qrs. : Iqrs, \ 43 d*.-f For 24i/ds. 2qrs.=9Sqrs. And '7^yds,=30qrs, Then 98X7X17371== 11 91 925 the dividend. And 30X 3=9p the'^divJBor. Then 1191925-^-90=gl32 4Scts,+s Ans. (11) Thus 20^. : 62h. ) : : Ubu, : 605w. 3pe. S^^^. 1;?^ 22 J. : 3Gc/. 5 +86 For 62 X 38 X 12=26784 the dividend. And 20 X 22=440 the divisor. Then 26784-t-440=606w. 3pe. 2qts, IpL+^iie Alls. For 563X 18X6=182412 the dividend. And lOOx 12=1200 the divisor. . Then 182412-^ 1200=1^152 Olct Ans. (13) Thus 8/.. : -20/.. ) , ^ ^^^ , ^^^^ ^^^^^^ 3^^^^ 7m. : 17771. ^ ^ For 20 X 17X6=2040 the dividend. And 8 X 7=56 the divisor. Then 2040~5G=3GT'. QcwL 2qrs. Sibs, Ans. (14) Thus2y./.. : 50t/r/.. ) .^^j^ . ^^,^^ [yqrs. : 3qrs. ^ For 50X3X 1=150 the dividend. And 2 X 5=10 the divisor. Then 150-:- 10= 15/6*. Ans. For 9QX 3X7=20 16^ the dividend. And 21 X 32=672 th(* divisor. Then 2016-^672=3. Ans. DOUBLE liULE OF THREE. 7 1 (16)Thu^4m.: Um.K,^ giOO : §360 For 1 2 X 9 X 100=10800 the dividend. And 4x7-^=30 the divisor. Then 10800~30=$|60. Aiis. (17) Inversely thus 40ft. ) : J 20ft, ) 54ft. 5 : I i^4ft, > : : lOd. : Id, lO^krs. 127)1. : 21m. ) For 20X54X27X i 0=29 1600 the dividend. And 40 X 54 X 72=155520 the divisor. ^ Then 29 1600^1 55520= Ic?. 10 J/tr5. Ans. (18) Thus 305^.^ : lOj^^^l' j:: sp^ .. ll6J.-f254Q For 1 056 x" 14X30=443520 the dividend. And 305 X 121=38121 the divisor. Then443520^3812l=116cZ. Ans. (19) Thus $210 : g837 ) ^. 07 or ^r r 15w. : 4m. 5 For 24w. ^d.=llld. And 837X4X171=572500 the dividend. And 210X 15=3150 the divisor. Then 572508-h.31 50=1 81(i.=25wj. 6c?. +2358 Ans. For 5X30X50=7500 the dividend. And 2ix 15— 371 the divisor. Then 7500—37^=^200. Ans. (21) Thus 5m. : 34m. J . , g^^ ^^ ^^^^ , ^3^3^ ^^ ^^^^ For 34X90X2050=6273000 the dividend. And 5 X 4=20 the divisor. Then 6273000-^20=^3136 50 ds. Ans. (22) Thus 24a..: ^760.. J ^, ^,3 . gj^g , ,,,,.+ , ,o For 76X121X18=165528 the dividend. And 24X45=1080 the divisor. Then 165528^1080=^153 26 cf^. Ans.+ 72 DOUBLE hULE br THREK. (23) Thu.42.a, : 392^^^^^ For 392X7X6=10464 the dividend. And 42X 14=:=588 the divisor. Therefore 16464— 588=28^72. Ans. (24) Thu« S^cut. : ^t.K,p,,as.:$m-!lilcU.i For r>Ox 150 X 050=7126000 the dividend. And 35X20=700 the divisor. Then 7125000-^700=^101 78 J ds.-f Ans. (25) Thusgll 15ch. : ^31 UVids. } :: gl25:g60356; 97n. : lyr. 6mo. ^ d^'.-f For 3118j=12475(/r*.X 18m. X 125=28068750 the dividend. And $11 75d^.=4700^r*.X 9=42300 the divisor. Then 28008750-f-42300=g663 56jds.-f Ans. (26) Thus glOO : g275 } . . hj.. . ^7, 12m. : 56m. ^ ' ' »^ ' fc^^ For 275X56X6=92400 the dividend. And lOOx 12=1200 the divisor. Then 92400-r 1200=^77. An^. (27)Thu8g56 :P ),,p,0:POO For 6 X 20 X 560=67200 the dividend. And 56X12=672 the divisor. Then 67200-^-672=^100. Anjb'. (28) Thus 12yds. : 75y^.. ), .^^^ . ^3^^,^ ^.^^^^ 59)'*. : 3qrs. \ For 75X3X5=1125 the dividend. And 12 X 5=60 the divisor. Then 1125-r60=18/6. 12or. Ans. PRACTICE. PRACTICE. EXAMPLES. (3) !at?- 148 74 CASE 1. (4) |I|l|3268atl Ans. ^16 34 cts. Ans. $2 22 cts. (^) 4260 at J 2130 1065 Ans. g31 95 d^. (7) |2l||634 at 2 miZ/5. Ans. $1 26 8 (6) 111115324 at 1 Ans. $13 31 cts. 73 (5) 352 at 4 mills, 70 4 70 4 Ans. gl 40 8 (9) |5m3456 at 5 miZZ5. (10) Ans. $17 28 498 at 6 mills, 249 49 8 Ans. $2 98 8 74 (11) I'KACTICE. 8462 at 8 mills. 4231 1692 4 846 2 (12) 1264 at 7 milk, 632 252 8 Ans. ^67 69 6 (13) Ans. $n 84 8 4628 at 9 mills. 2314 923 6 925 6 Ans. $41 65 2 CASE 2. cf5. d$. (2) |6|| iVi3648 at 6J d*. (3) llO|yVp42 at 10 ds. Ans. $228 Ans. $74 20 cf*. d5. (4) |20m8264 at 20 ds. Ans. $1652 80 ds. (6) |50|1|5876 at 50 ds. (7) Ans. $2938 386 at 25 ds. (5) |25p Ans. $96 50 ds. 25 20 3542 at i:. c.'.. 885 50 708 40 Ans. $1593 90 (8) i'KACTICE. ds. 50 25 5 r31925 at 80 c/5. 15962 50 7981 25 1596 25 Ans. ^25540 00 ci8. (9) |12im4264at 121 d*. Ans. g533 (10) cts, 50 dL ^\ 18626 at55d*. (11) 9313 931 30 Ans. ^10244 30 (12) cts, 10 528 at 16 els, 52 80 26 40 5 28 Ans. ^84 48 (13) 25 J 1724 at 371 cts, 1 431 215 50 Ans. g646 50 cts, 50 j ^¥8 13854 at 56 J ds. 6927 865 87 5 Lns. ^7792 87 5 4858 at 29 cts. Ans. gl408 82 (15) cts, 50 2267 at 85 els. 1133 50 666 75 226 70 Ans. gl926 95 76 PRACTICE. (16) |20J»|190at20cf5. Ans. g38 (17) cts, 6 3654 at 18f c<#. 456 75 228 37 5 Ans. $685 12 5 cts. (18) 50 117638 at 70 c«5. 8819 1763 80 1763 80 Ans. gl2346 60 (2) $ cts, 10 25 10 102 50 5 12 5 64 Ane. gl03 26 5 CASE 3. (3) cts. 4 15 7 29 05 2 07 5 1 03 7 51 8 14 8 3 7 Ans. $32 86 5 PRACTICE. 77 Cwt. qr. lb, ^ cts, (4) 129 1 10 at 1 05 129 (6) Ans. gl35 80 4 Cwt. qr, $ 130 1 at 15 130 450 15 1950 3 75 Ans. gl953 75 qrs, lb, cts, (8) 2 14 at 2710 (5) Cwt.qr, g cts, 16 2 at 5 18 16 3108 518 82 88 2 59 Ans. g85 47 Cwt, qr, lb, cts. (7) 25 1 9 at 175 25 ll I- 875 4. [350 4, -43 75 43 7 I: 6 2-f 6 2+ 1 5+ Ans. $44, 32 8 (9) lb, oz. dwt, gr, 6 5 10 5 at 1355 338 7 Ans. gl6 93 7 g cts, 4 16 6 2496 138 6 34 6 17 3 3 Ans. g26 86 8 G2 78 PRACTICE Ih. oz. dwi.gr, cis. . lh,oz. dwt.scr, cts. (10) 27 10 4 18 at 2635 (11) 9 11 17 22 at 613 27 9 6 ^ 18445 ^ 5270 4^5517 1 ^ 306 5 10 5 2\ - 204 3 51 3 i711 45 1 1 13 17 5 : 25 6 4 ]r 6 58 7 12 J 12 7 12 \ 2 19 5 6^ 5 1 6 V 43 9 - 5 4 2| 12 2^ 6 . 2 7 2 2 Ans. g733 92 7 Ans. }ei 24 -3 oz. dwL gr, cts. yd, qr. $cts. (12) 816 13 12 at 12^ (13) 27 3 at 9 65 1 1 816 1 27 10 i 1632 816 408 2J 6756 1930 260 65 4 82 6 102 00 U 2 \ 6 2 2 41 2 j \\ 12 J 6 3 II 12 Ans. J267 78 7 A ns. gl02 08 3 = PRACTICE. 79 yd, qr, cts, (14) 860 1 at 84 860 (16) 5040 672 722 40 21 Ans. $122 61 gal, qt, cts 428 3 at 140 428 1120 280 560 599 20 70 35 Ans. $600 25 (15) yd. qr, na, cts, 126 2 2 at 475 126 2850 950 475 598 50 2 37 5 59 3 Ans. 5^601 46 8 gcU, qt. pt, cts. (17) 765 3 1 at 21 8 J 4 875 765 4375 5250 6125 6693 75 4 37 2 18 1 09 4)6701 39 Ans. $1675 34J 80 hhd, g'al. (18) 5 PKACTICE. $ Qts, 31| at 47 12 3H ^ 5 233 60 23 56 AnB. g259 16 hhd, gaL qt. ^ ds, (19) 17 15 3 at 64 75 17 (20) bu, pe, cts. 120 2 at 35 120 700 35 Ans. 4200 17 5 42 17 5 hu. pe.qt.pt. cts, (22) 1354 1 5 1 at 25 1354 100 125 75 25 338 60 6 2.1 3U 3i^ Ans. ^338 60 5} 453 25 647 5 1100 75 9 25 3 08 3 3 08 3 77 1 (21) Ans. g llie 93 7 hu, pe. qt. ^ cts. 780 3 2 at 1 17 780 9360 819 912 60 58 5 29 2 7 3 ^. Ans. ^913 55 R, P, (23) 35 2 18 at 54 35 35 16 27175 16305 1902 25 27 17 5 5 43 5 67 9 Ans. gl936 53 9 PRACTICK. 81 A.R,P. $ cLs, (24) 146 3 10 at 35 10 146 A. R.P. $ ds. (25) 750 1 4 at 12 25 750 21060 14040 3510 5124 60 17 65 8 77 5 2 19 3-f. 61250 8575 9187 50 3 06 24 30 6| AnB. $9190 86 8| Ans. $5153 11 8-f APPLICATION. Cwt.qr.lb, i cts, (1) 84 2 14 at 10 60 84 CwLqr.lb, cts, (2) 17 1 7 at 1212| 2 14 4200 8400 882 00 5 25 1 31 2-f Ans. $888 66 2-f 2425 halves. 17 16975 2425 412 25 6 06 1^ 1 51 5| 2)419 83 8 mills. Ans. $209 91 9 mills. 82 T.cwLqr. $ ds. (3) 15 10 3 at 80 15 15 PRACTICE. yd. qr, pie, yd, (4) 35 2X170=6035 at} 6035 10 40075 8015 1202 25 40 07 5 2 00 3J 1 00 U 4)6035 qrs, Ans. p5 08 Ans. gl245 33 0| A, R, P. $ ds, (5) 175 3 12 at 52 15 175 26075 36505 5215 9126 25 26 07 5 13 03 7 3 25 9 65 1 Ans. $9169 27 2 (6) 1365 at ld,=$6 82|c^. Ans. (7) 784 at 84 di. 784 336 672 588 Ans. g658 56 PRACTICE. 83 (4) [l[j|475at| 12)118f STERLING MONEY. CASE 1. (5) mi[299atj 12)149| Ans. 9*. lOfdf. (6) Ans. $l2s, 5|cf. 978 at I 489 244^ 12)7331 210)6|1 1 Ans. £S Is. Ud. (2) 1241978 at 2d, 2|0)16|3 Ans. £8 3^. (4) [6j||792 at 6d. 2|0)39|6 Ans. £19 16^. CASE 2. (3) 499 at 5J. 166 4 41 7 (5) 2|0)20|7 11 Ans. £10 7*. Ud. 1 888 at 9d. 444 222 210)66|6 Ans. £33 Ss. 84 (6) PRACTICE. 921 at lid. 460 6 230 3 153 6 2|0)8414 3 Ana. £42 4*. 3d, CASE 3. (2) |3|||487 at 15d. I I |l21 9 2|0)60I8— 9 Ans. £30 8*. 9c?. (3) 979 at 22J 489 6 244 9 81 7 20 4£- 2|0)181|5 2J Ans. £90 15*. 2|cf. (4) 532 at 23j 3X9=27 2' 1^ 14 J 7) 1 ^ -13 8 9 19 2 9 7 49 24 4 t 1 14 4 1 8 13 0| 9 7 17 6J 14 5-f 7 21 £» 1 Ans. . ei5 5 i Ans. £79 1 8? 1 1 TARE AjN'D tret. 87 TARE AND TRET. CASE 1. CwL qr, lb, Cwt. qr. lb. Cwt. qr. lb. (2) 7 3 20 (3) 6 2 5 (4) 369 2 21 8 «— 1 11 —10 1 12 gross 63 1 20 Ans. 6 22 Ans. 359 1 —5 1 19 Ans. 58 CwLqr.lb. C.qr.lb. lb. (5) 6 1 19^ (6) No. 1.3 2 19 tare 34 8 No. 2. 6 13 tare 57 No. 3. 4 3 5 tare 46 43 1 12 whole gross. — C.qr.lb. —2 23 tare. 14 2 9w.t.l37==l 25 —1 25 Ans. 41 17 neat. Ans. 13 1 12 CASE 2.' C. qr. lb. qr. lbs. (2) 4 2 24 2 18 7 7 33 gross. 4cwt. 2qrs. 14^6*. whole tare. 4 2 14 tare. ^ Ans. 28 1 14 neat. TARE AND TRET. (3) C. 21 3 qr. 11 2 2 1 \ J at 5 50 Neat 18 2 t -^ % *. i 4400 550 lb 1 1 2 9900 275 9 8+ 4 9 Ans . glOl 89 7 (4) 2 qr. Ib.^ 1 25 9 lb. 30 9 C. 9r. lb ross. 270=2 1 18 re. $cts. t 5 10 19 22 2 1 Ig] 1 18 ta Neat 19 3 11 a qrs. ^ i 4 ? 45 i 51 ( )0 ) )0 )5 11 5 M 8+ 8 2-f- 96 i 2 £ 1 S 1 Ans. $ 101 22 5 value. TARE A3SD TRET 89 CASE 3. C. qr. lb. (2) 7 3 14 4 lbs 31 2 gross. 4 2 1 14 5 2 14 tare. Ans. 25 3 14 neat. C. qr, lb, (3) 5 1 13 10 lbs. 16 53 2 18 gross. 7 2 18+ tare. Neat 46 at 8 75 46 5250 3500 Ans. ^402 50 value. H,^ '90 TARE AND TRET. (4) 4C. Iqr, 24/6. 26 3 4 gross. Tare 4 l Neat 22 1 8+ 25+ Ibi. 27=2519 at 74 — 7j - 17633^ 1259 5 Ans. $188 92 5 value. CASE 4. (2) 2C. Xqt, lOlb, 12 lbs. 28 8 gross. 4 2 1 tare. 7 suttle. 17 tret. Neat 22 2 18 at 19 60 — — 22 lbs. 14 2 2 39 20 392 431 20 9 80 2 45 35 35 Ans. g444 15 value. (3) I"' ' = TARE AND TRET. C. qr, lb, 4 1 11 6 91 gr, lb, 1 5 6 iie 10 ^ 13 2 tare. cwt, 13 2 tare. ^)24 1 8 suttle. "^ — 3 20 tret. $ ds. Neat 23 1- 16 at 6 75 ^ 23 qrs. 1 20 25 135 155 25 1 68J 84;- 12 Ans. gl57 90 value. APPLICATION. C, qr, lb, (1) 17 3 22 gross. 3 14 tare. ' — lbs, ds. Neat 17 8=1912 at 23". 5736 3824 478 Ans. g444 54 92 (3) (2) 5C r 8" K Neat 7 C.qr. 6 3 7 5 3 8 TARE AND TRET. \ 2qr. 19Z6. 3X5=15 i 2qr. 25/6. 3 No. 1. No, 2. No. 3. No. 4. 7 1 2 5 19 5 3 5gl 3 3 11 ta •OSS. C.IO 3 11 tare. t g6 75d^. 74 le. 4 22 a 16^ 2- - 27 00 472 5 499 "50 r 96 z 24 12 /6. 18 10 26 3 A grog tare atj ns. g500 82 vail 8 4 tV i 28 1 s» ^3 75c<^. 2 1 Neat 3 25 1 lb. 1 rh 3 3 18 ' 75 ( 93 ' Ai IS. ^ 93 78 3 value. (4) TARE AND TRET. IC. tqr, 23lb. 4X6=24 93 5 3 34 3 20 gross. 3 3 12 tare. 18^6. 24 72 ^ C.qrAb, 432=3 3 12 tare. Neat 31 8 at $5 l'7^cls. 2 1035 halves. 31 1035 3105 32085 73 9 2)32168 9 Ans. 79 4 value. (5) IC. l^r. 13Z&. 3X5=15 4 11 5 20 1 27 gross. 2 3 22 tare. 22/6. 15 110 J!«. C.qrJb. 320=2 3 22 tare. Neat 17 2 5 at $9 64ctg. — 17 2 1 2 67 48 lb. 96 4 163 88 4 A 4 82 1 5^ 34 4 8 6 Ans. g ,169 13 94 inte:^est. a qr, lb. (6) 6 2 14 10 lbs. 66 1 gross. 9 1 24 1 20 10 2 16 tare. 55 2 12 suttle. 2 16 tret. lbs. cts. Neat 53 1 25=5989 at lU "i 65879 2994 5 Ans. ^688 73 5 value. -MtoQeiM INTEREST. EXAMPLES IN CASE 1. (2) 225 7 $ cts, (3) 384 50 5 Ans. 5515 75 Ans. gl9 22 5 m. INTEREST. 9& £ 8, % cts. (4) 580 10 (5) 1654 81 6 5 r- J6 *. eif. %cts. £34 83 Ans.34 16 7 g82 74 05 Ans. 82 74 20 5.16 60 12 rf.7 20 ^ j6 £ s. d» (6) IllillSOO (7) 350 ^Ans. 18 7 6 Ans. $1 50 1750 87 10 £18 37 10 20 ^.7 50 12 d,e 00 (8) |J|524 (9) 111842 2620 4210 131 421 Ans. g27 51 Ans. g46 31 96 XNTEKEST. CASE 2. $ £ s.d, £ 8, d. (2) 540 (3) 124 5 6 4 19 5 Int for 1 year. 5 4 3 27|00 £4197 2 £14 18 3 Ans. Ans. g54|00 «.19|42 12 rf.5|04 ; (4) 482 6 g28f92 interest for 1 year. 7 Ans. g202|44 CASE 3- (2) 325 4 mo. 2 , ^ 13|00 Int. for 1 yr. 4 ; i 52 Int. for 4 yrs. 2|16|6 Int. for 2 mo. Ans. $54 16 6 1 INTEEE8T. 97 (3) 840 4 33160 Inti for 1 yr. 6 168 8 00 Int. for 5 yr. 40 Int. for 3 mo. Ans. gl76 40 (4) mo. 4 840 7 58|80 Int. for 1 yr. 5 294|00 Int. for 5 yrs. 19|60 Int. for 4 mo. Ans. $313 60 (6) 1200 5 Ans. g60 00 Int. for 1 yr. Then say, nslyr.: 15w. ^ $^^ '• $^'^ 30c<5. Ans. (7) 240 960 120 60 Ans. gn 40 Int. for 1 yr. Then say, as lyr. : 61d. gll 40: gl 90cfe. Ans. 98 INTEREST. £ (8) 1000 7 £70 00 Int. for 1 yr. Then as lyr. : Umo. : : je70 : £81 13*. Ad Ans. (9) 450 51 2250 225 $U 75 Int. for 1 yr. Then as \yr. : 6mo. 20d. : ; g24 ISds. : $13 15cts.+ Ans. $ cts. (10) 375 25 6 ^22 51 50 Int. for 1 yr. Then as lyr. : Syrs. 2mo, 2w, 5rf. : : g22 Bids. 5m, : $72 85. Ans. CASE 4. (2) 854 30 6)25620 Ans. ^4 27 (3) $ 1100 48 8800 4400 6)52800 Ans. $S 80 INTEREST. 09; $ (4) 3459 75 $ (5) 1500 60 17295 24213 6)90000 jl 111 15000171. at —2500 1 6 per cent. 6)259425 Ans. g43 23 7 Ans. gl2 50 CASE 5. (2) 6 yrs. 4 dolls. 24 Int. of jSlOO for 6 yrs. -flOO £124 amount of £100 for 6 yrs. Then as £124 ; £1240 : : £100 : 1000. (3) 6 yrs. 6 dolls. Ans. 30 Int. of glOO for 5 yrs. 100 gl30 amount of glOO for 5 yrs. Thenasgl30 : $2470:: $100: $1900. Alls. (2) CASE 6. $ 1476 amt. 1200 prin. $276 Int. And gl200 : $100 : ; time. Then as byrs. 9mo, : $276 : $23 int. of $100 for the i $23 : : lyr. : $4 per cent. Ans. same 100 INTEREST. $ cts. (3) 927 82^ amt. 834 00" prin. ^93 8;21 int. As g834 : §93 ^^cts777pQ^Q : gll 2octs. And then, as 2yr*. 6mo. : §11 2bcts, : : iyr, : §4| per cent. Ans. CASE 7. £ £ (2) 1600 2048 4 1600 £64 00 : Iyr. : : 448 : tyrs. Ans. (3) 1000 41 40 00 5 00 §45 00 : Iyr. : : §281 25ctjf. : 6yri, 3f»o. Ans. COMPOUND INTEREST. § (2) 760 prin. * 6 rate per cent. 45 60 int. 1st year. 805 60 amt. of let yr. and prin. for the 2d yr. 48 33 6 int. of 2d yr. 853 93 6 amt. of 2d yr. and prin. for the 3d yr. 51 23 6 int. of 3d yr. 905 17 2 amt. of 3d yi;. 760 00 1st prin. Ans. §145 17 2 compound int. INTEREST. £, s. d, £ 8. d. (3) 242 10 6 242 10 6 6 14 11 Oint. Istyr. lOll £14|55 3 257 1 6 amt. 20 15 8 5| int. 2d yr. 11|03 272 9 ll|amt. 16 7 int. 3d yr. 288 16 1 If amt. 17 6 7i int. 4th yr- 306 3 7 amt. ^242 10 6 1st. prin. Ans. 63 13 1-f com. int. (4) 1300 5 •65|00 int. 1st yr. 1300 1365 amt. 5 68|25 int. for 2d yr. 1365 1433|25 amt. 5 71 66|2 int. for 3d yr. 1433 25 Ans. gl504 91 2m. amt. - u— ■— 102 $ (5) 3127 INTEREST. t 3127 140 71 5 int. of , the 1st yr 12308 1563 5 3267 71 5 amt. 147 4 7 int. 2(1 yr. gl40 71 5 3414 76 2 amt. 153 66 4 int. 3d yr. 1»R( $ Cts. (1) 620 25 3568 42 6 amt. 160 57 9 int. 4th yr. Ans. g3729 00 5 amt. JMISCU0U8 EXAMPLES. (2) 420 7 3101 25 310 12 £29 40 20 nt. for 1 Jrr. *.8 00 Ans. je29 8* $ 1450 60 34 11 37 i 5 Ans. gl70 5B ^m (3) 6)87000 14500 mills=gl4 hOds. Ans. INTEREST. 103 £ s. (4) 626 5 3131 5 156 11 3 £ s. 626 5 32 17 d, 6Jint. of the Istyr. 659 2 34 12 6| amt. 1 int. of 2d yr. £32187 16 3 20 693 14 36 -8 7f amt. 5 int. of 3d yr. «.17|56 12 rf.6|75 4 Ans 730 3 —626 5 OJ amt. prin. . £103 18 0|+ compound mt. fr*.3|00 £ (5) 1659 4 r£66|36 20 Int for 1 yr.. «.7|2e 12 £^.2|40 4 5r.l|60 Then as 365 days : Ans. 21 days : : £66 7^. S^rf. : £3 16*. 4j(f.+ 104 INSURANCE, COMMISSION AND BROKAGE. (6) 500 8 840 00 int. for 1 yr. Then as g40 : gSOO : : lyr. : 12yrs, 6mo. Ans. (7) Thus, Qyrs. and 6mo. at 2 per cent. =^13 interest on glOO. Then ^13+gl00=:gll3=amount of glOO. ^ And as gll3 : p50 : : glOO : g221 22ct8. 9m. Anfl. £ (8) 450 amount. 300 principal. £150 interest. Then as £300 : £100 : : £150 : £50 which divided hy the 5 years=10 per cent. Ans. INSURANCE, COMMISSION AND BROKAGE. EXAMPLES. £ (2) 1320 5 Ans. £66|00 (3) 3450 41. m 13800 1725 $ 1680 n 3360 840 420 Ans. $l55\25cts. g46|20 commifl . gl680— g46 20cfe.3=gl633[80cf5. Ans. £ (5) 7G0 INSURANCE, COMMISSION AND BROKAGK. $ (6) i ^ 5630 n 4560 380 £49140 Axis. £49 8*. 20 «.8|00 39410 2815 1407 5 Ans. g436|32|5m. 105' 17654 181 141232 17654 8827 4413 Ans. g3310|12. (8) 2150 Ana. £43100 $ cU, (9) J |||984 50 984 50 246 121 Ans. gl2|30|62l (10) i iJllSsO 75 " U li 1650 75 825 37! Ans. g24|76|12i 106 DISCOUNT. DISCOUNT. EXAMPLES. (2) Thus, 2mo. at 6 per cent. per an.=±gU int. of glOO + 100"' 1011 amt of do. •■ Then as glOlJ : g850 : Ans. : glOO : g837 43cts. 8w.+ (3) Thus, 9r/io. at 6 per cent. per an.=g4i int. of g 100 100 1041 amt. of 100 Then as ^ present ,1041 : g645 worth. :: glOO : ^61 7 22cts. 4m. 645 00 Ans. $21 11 6 (4) Yrs, 4 5 20 int. of 100 glOO for 4 yrs. gl20 amt. of do. en as ^120 $115 SOds. : glOO : ^646 25ct8, Ans. J/ Sino. at 6 per cent, per an.=^4 int. of ^100 100 gl04 amt. of do. Then gl04 : ^580 : : g 100 : $551 69f^*.-f- Ans. DISCOUNT. 107 Yrs. 12 ii 131 int. of 100 100"' gllSiamt. of do. Then as gll31 : g954 : : glOO : $U0 52cts. 8m. Ans. (7) Thus, 15 mo. = l^yr, at 7 per cent. num=g8| the discount of 100. 100 per an- glOS^amt. Then gl08| : g205 sent worth. : : glOO : gl88 BOcts, 205 00 5m. pre- Ans. ^16 49 5 (8) mo, 6 I 2 5 3 i s 3f discount of 100 100 gl033 amt. Then as gl03f : g775 : : glOO : $146 9Scts. 7m. Ans. 108 (9) mo» £ 1 DISCOUNT. mo. £ Again | 3 |JI6 H 15 7710. 5 dig. of lOafor lOmo. 71 dis. of 100 for 100 100 Jl05 amt. 1074 1005 —475 Rem. 530 Then as 105 : 475 : : 100 : 452 38. Ans. to first part. Again 1071 : 530 : : 100 : 493 02 4 Ans. g945 40 4m, (10) 2260 6 Again 6 5 135 60 int. fori yr. 5 678 00 int. for 5 yrs. 30 dis. of 100 100 |Jl30 amt. Then gl30 : te60 : : glOO : gl738 46cts, Sim. pres. wr. 2260 00 521 63 8 discount. 678 00 interest. Ans. ^156 46 2 EQUATION. 109 (12) 782 (13) 476 (14) 1335 4 3 6 £31|28 Ans. $U\2iicts, 33 10 dis. 20 1335 00 *»5|60 Ans. £31 5s. 7J. Ans. jJlSOl 90cts, 12 d.l\20 650 4-* 2600 325 29 1 25 discount. 650|00 Ans. g620|75 EQUATION. EXAMPLES. t (2) 250X6=1500 250X8=2000 500 3500-^500=:7mo. Ans. no BARTEK. (-3) £ 100x2=200 100X4=400 100X6=600 300 1200-f.300=4mo, Ans. (4) 100X3= 300 200X5=1000 • 250X8=2000 550 3300-^550=6/na. Ans. -^*^«^- BARTER. EXA:\irLES. (1) Thus 2c Then as wl. 2qrs. 13/6*.=±.?93/6a. X 0c/*.=:2637c/*. 25cts, : 2637c/*. : : 1/6. . 105/6*. moz, Ans. (2) Thus 2500/6«.X4^c/5.=^112 50d*. Tiien as ^1 SOci^.l ^112 50d*. : : 1//^ : 86/6*. 802:.+ Ads. (3) Thus 10a/5*.X5?1 25r/.9.=r^t35 OOc^*. Then as U'icts, :'gl35 mcU, : : lib, ; 1542/6. 13o^.+ Ans. (4) First, as \cwL : $3 75s. at 20cfs. per lh.= 50 00 10 loads X 156?/. X 45cc^*.= 67 50 And fi5gah. at the rate of g75 per hhd.=lO\ 19 —868 69 1053 15 Rem. unpaid gl84 46 Then30d^. : ^184 4Cd*. :: lib. : 615Z6*. nearly. Ans. LOSS AND GAIN. EXAMPLES. (2) Thus lOds. —a 2 Then 1/6. : 17G3/6.f. : : 2ds. : p5 2Gch. Ans. LOSS AND GAIN. 113 (3) Thus g5 2^cts. ~5 00 25 gained per barrel. Then Xhar, : 3636ar. : : 25cts. : $dO Ibcts. Ans. (4) Thus g3 90c^^. —3 75 15 gained per yard. Then lye?. : \BQyds, :: 15c^5. : g22 50c/*. Ans. (5) First, IcwL : g7 SOr/^. : ; ISaof. 2^r*. : gl38 75d*. the cost. Then U^t, : %1 ISds. : : 18cw/. ^rs. : ^143 37icf*. sold for. Ans. gained ^4 62| (6) First, 210 rcam5X$2 621=^551 25d5. the cost. And 210ream*x|2 87|=|603 75ds. sold for. Ans. g52 50 gained. (7) Thus, sold for $20 Ibds, cost la 12j gained g2 62| Ans. (8) First, 50cf*. —45 5 Then 16m. : 1506w. : : Bcis. : p 50cts. 1st Ans. Again, BOcts, : 5cts. : : glOO : glO. 2d Ans. K 2 114 LOSS AND GAi:^. (9) First, 760/6*. X 90d.9.=g684 00 sold for. 810 00 cost. Lost 126 00 1st Ans. -J ThcngOlO : $126 :: ^100 : gl5|. Ans. (10) First, Slllds. Then 31^cts. : B^cts. : : $100 : gl4| per Cent. Ans. (11) Thus 15. : 2(1 : : £100 : £162 per cent. Ans. (12) Thusgl3 75d.?. First cost of each piece. 3 12^ for dyeing. gl6 J]7| whole cost. ThenglOO : $112 :: $16 871d*. : $18 90ci*. Ans. (13) Thus Iciof. : 1/6. :: $7+$3 : ^cts. 9m. Ans. (14) Thus, paid 22cts, per lb. Sold it for 19 Lost 4cts. per lb. Then as 1/6. : 702/6*. : : 4cts. : $28 OMs. Ans. (15) Thus S2 23c/*. : $2 75c/*. :: $110 : $135 65c/*. And $135 65c/*.— $100=:$35 65c/*.=:35|- nearly. Ans. ' (16) Thus $100 : $125 : : $2 lOcU. : $2 i62lc/*. what 1 hox sold for. Then as $3 50c/*. price of Icwt. : $2 62^/*. price of 1 box :: 112/6*. : 84/6*. Ans. LOSS AND GAIN. 115 (17) First, lOpie. X gl4=g224 the prime cost. And 5pie.X$ll=:$H5 6pie.X$i5=^pO ^175 received back again. Then as ^100 : gll2 : : g^24 : ^250 SSds. price of the whole with rate per cent, added. — 175 00 5)75 08 price of the 5 pieces. Ans. gl5 17 G perpze. (18) Thus ^500—^410=^90 gain on the whole. Then as 31211)8, : lib. : : ^a0:24d*. Iw.-f Ans. 19) Thus $1 : glOO : : 5cts. : $5 00 the Ans. (20) First, ^1 05r!.«f.X5l0— ^535 50d*. prime cost. And ^1 30ci6\XiA0—^QC)3 OOcts. sold for. mo, 3 6 1 50 100 00 glOl 50 Then glOT BOds. : glOO : : ^,663 : $^353 20cf*.+ Hence $653 20c^«. — ^535 50r^. = ^117 70^5. Ans. 116 FELLOWSHIP. FELLOWSHIP. EXAMPLES. CASE I. (2) Thus D.'s stock ^500 E.'s 400- F.'s , 300 Sum 1200 Then as t^OO : 500 : : 300 And 1200 : 400 : : 300 And 1200 : 300 : : 300 (3) ^ Thus A. ^1200 B. 600 C. 700 Then as 2400 as 2400 as 2400 Whole debt ^2400 1200 600 700 125=D.'s ] 100=:E.'S 75=F.'s ^ Ans. 1800 1800 1800 900 375 525 Ans j^lSOO proof. (4) Thus A. had 50 ca«/c. B. 80 C. 70 Sum 200 cattle, cattle. Then as 200 ; 60 as 200 : 80 as 200 : 70 $60 proof. (5) FELLOWSHIP. $ Thus, to A. 120 B. 250 75 C. 300 D. 208 25 Sum 879 00 117 Then j As j5879 : g650. $ 120 : 88 754-=A.'ssh. 250 75 : 185 42+ =:B.'s sh. 300 : 221 84+ =C.'8 sh. 208 25 : 153 99+ =D.'6 sh. ■ Ans. (6) Thus A. is to have 1 portion. B. 2 C. 6 9 sum of the portions. Then as 900 : lOOrrrA.'s share. 900 : 200=B.'8 share. 900 : 600=C.'s share ii Ans. (7) Thug, he owes to A. 250 50 B. 500 00 C. 349 50 Sum 1100 00 Then As 1100 : 960 $ cis. f cts.m. [250 50 : 213 61 8+ A.'s ; 500 00 : 436 36 3+ B.'s [ 349 50 : 305 01 8+ C.'s ' Ans. 1 1^ FELLOWSiriP. EXAMPLES CASE 2. % (1) Thus 8«X3= 264 120X4— 480 300X6=1800 Sum of stocks and time 2544 % i i cts.m, C 264 : ; 184 : 19 09 4=L.'s ) Then as ^2544 : \ 480 : •,. 184 ; 34 71 6=M.'s > Ans. ( 1800 : : 184 : 130 18 8=N.'s ) $ m. $ . $ m. ^ (2) 580X3=1^740 480x3=1458 + 100 —300 680X9=6120 180X2=372 +500 A.'s product 78fJ0 686X3=2058 % m. $ —400 1000X9=9000 + 200 286Xl=:286 + 1000 1286X3:=3858 C.'s product 8032 % A.'s 78<50 B.'s 12600 C.'s 8032 g ^ cU.m, % (tx. C 7860 : 581 64 8+A ) . 28492 : 2108 44 ::} 12600 ; 932 41 4+B >'^^^* .( 8032 : 594 37 7+C ) 1200X3=3600 B.'s product 12600 EXCHANGE. 119 EXCHANGE. DOMESTIC EXCHANGE. (1) Thus, £63 Us, 6d.~152Ud~T2d. a dollar in Vir- ginia=:^212 4lJc<*. Ane. (2) Thus, £230 10^. 'rd.=5532'7d.~9Gd, a dollar' in New York and N. Carolina=g576 S2cts, 2m. Ans. (3) Thus, ^150 90^.=a doll. Penn. cur. 12)13500^. 2|0)112|r> £56 5.9. Ans. (4) Thus, ^377 40ds. 72c?. =a doll. Mass. cur. 754 80 26418 12)27172 80 2j0)225|i 4d, £113 4;?. 4d. Ans. (5) ^ Thus, g389 45cts'. 56 numer. 90-f- 9=10X5=50) ThatisJJ^fJ. Ans. CASE S. ^2) First lib. troy=240t?io«. therefore | of aiir=x2T?F= ;f^a. Ans. (3) Thus 3xlXl_ 3 Anc? And 8x4x4-~^^- ^'^• (4) Thus lkhd,=:SO^ts, therefore | of shF^iwsJ''^^' Ans. (5) Thus 8/«r.=lm. therefore 9x1=9 the numer. and 16 X 8=128 the denom.=y|^. Ans. CASE 7. (2) Thus 2X112=224 the numer. and 252x1=252 the denom.=f||=|/6. Ana. (3) tIht of £l=Tifff^ of ^r ==l^ll=^^- Ans. CASE 8 (2) Thus J of a Bhilling=5 of y=y =10|(/. Ans. (3) Thus If of a day=|| of \^—%\^—^hrs. Ans. (4) Thus fg. of an acre=TV of | of |-''=Vi" perches= Ir. lOp. Ans. CASE 9. (2) Thus bs. 4^.=64J. and £l=240<^. therefore 4\= y\£. Ans. 124 VULGAR Fractions. (3) Thus Cmo. 2w.=26iv, and lyr.=52w. therefore || oriyr.=:|yr. Ans, (4) Thus 2qrs. 3/i«.=llna. and lijd,=^16na, therefore j}yd. is the Ans. ADDITION OF VULGAR FRACTIONS. EXAMPLES. (2) Thus t\+A+A+tV=H=1- Ans. (3) Thus 44-.iJ-f «=V=16. Ans. (4) Thus 6)5 10 1 2=10 common denom. And 10— 5X2=4) 10-10X5=5 P^"'^^- Whence A+tV^A- Ans. (5) Thus 3|=V, 8f=V% and 4x7x9==252 common denom. And 252—4X13= 819) 252—7x58=2088 >numer. 252-^-9 X 4= 112) Whence fH+WI+Ht='¥7?l=ll|H- Ans. (6) Thus i of |=H=A. andf of t^=^=/,. Then 8)16 24 2 3=48 common denom. And 48^16X5=15) „^^^ 48-^24x7=14 r Whence 4f+i|=o. Ans. (7) Thus iof -fof Y=»|«=53'per.=Ir. 13Jp. And ^ of V«=2f-«=28j[>. Whence \R. 13j/>. 28 Ans. 2 U VULGAR FRACTIONS. 125[ MULTIPLICATION OF VULGAR FRACTIONS. EXAMPLES. (2) ^ by 1 thus 2X 1=2__ ^ (3) Thus 6|=:26 by i=26xl^26_ 4X7=28" (4) 4f=V^ by f=19X2=38_ -=--y^. Ans. 4X3=12^^^=-^- ^"^- SUBTRACTION OF VULGAR FRACTIONS. EXAMPLES. (2) Thus ^ of 1=0^ whence ^J— Jg. 4) 20 28 5 7=140 common denom. 140—20x10=133. V numer. 19=133 > 1= 5[- 140-f-28X wnence y^-jy — jaq — to — a?* -^"S* (3) Thus 1X14=: 14 common denom. And 14-^ 1X5=70) 14-14x8= 8 r"^"""'- Whence 1^—^^=:Y^=4{^, Ans. (4) Thus I of a league=| of 3 miles=2 miles. And -^ of a mile= 7jf of 8 furlongs=:|^'==5-^ fur- longs=:5 furlong's 24 poles. Therefore 2m. — 5fur, 24/>o.=lm. S/wr. IGpo, i\ns. (5) Thus 5|='^3 and 2|=| therefore 4x3=12 com. d. And 12-f-4x 23=89) 12-f-3X 8=32 r'"'''^'' Whence f|— f|=ft=3^. Ans. (6) Thus 2 of "^^=1-1 and | of |=|^. And 4) 48 20 12 5=240 common denom. And 240~.48X 14=70 ) 240-20 X 3=36 P™^^*- 70 3 3 4 17 A «« 2Tff 2¥0 24^ T2 0* -^"S* 126 VULGAR FRACTIONS. DIVISION OF VULGAR FRACTIONS. EXAMPLES. (2)|by?tIiusJ)f(5V Ans. (3) 6|=^/-^lthusa)3J3(9/r=l9|. Ans. (4) Thus f of 1=-^ and 1 of |=f. Then T^-H| thus |)^tM='l- Ans. (5)^byfthus4)i(TV=f. Ans. (6)|ofi=iJand|of|=5V Then 4J by J, thus |')J-KW=16f Ans. (7) 1 of 17i=i of \'=^\'. - Then =y5-^1thus-J)-V(V2=llj. Ans. (8) Thus f of 91.p=.| of ^ry'^^f?!^- And l^i'^'if thus i^i^'nV{\\m^=3i^Uif Ans. RULE OF THREE IN VULGAR FRACTIONS. EXAMPLE.?. (2) Thus 3l.yds.=\^ and 9j.9.=|-9 and ^7jds.=Y' Then we have V = l"" = = '/ = l^*- 3 I ■ m il DECIHAL FRACTIONS. 129 REDUCTION OF DECIMALS. CASE 1. (2) 8)7.000 (3) 24)170(.70833+ 168 .875 Ana. 200 192 80 •72 80 72 •— 8 rem. (4) 2162.)3810(.1762+ Ans. 2162 (5)254)1160(.4566+ Ans. 1016 1440 16480 15134 1270 1700 13460 12972 1524 4880 1760 4324 1524 556 rem. 236 rem. ■■si. , .1 ■ ■■ ■■■Ja 130 DECIMAL FRACTIOIiS. CASE 2. (2) Thus 2i2. 4P.=84P. lwi.=160P. Then 160)840(.525 Ads. 800 400 320 800 800 (3) 2qr. 2na,=zlQm, Then 16)100(.625 >96 40 32 80 80 And lyd.=zl6na, Ans. (4) Ur.=:60wim. And 60)5.00(.08333-f Ans 480 (3) lo2r.=480^r*. Then 480)1 000(.02083-l- Ans. 960 200 180 4000 200 3840 180 1600 200 1440 180 160 rem. 20 rem. DECIMAL FRACTIONS. 131 (6) 2qts, \pl.—5pts, lhhd,=::S04pts, Then 504)5000(.1to992-f Ans. 4o36 4640 4536 1040 1008 32 rem. CASE 3. £ Day. GaL (2) .1361 (3) .235 (4) .42 20 24 4 «.2.7220 940 ^f.l.GS 12 470 2 qt,pt. Ang. ( 40 : : 133 : 35=C.'s ) 133 proof. (4) Suppose No. 3 cost 20 3 60=No. 2. 120= No. 1. 60 20 Result 200 Then 200 : 350 : 2lO=No. 1. 350 : 105=No 350 : 35= No, Ans. M 134 POSITION Yrs, (5) Suppose 60 2 120 3 5)360 3)72 24 result. Then 242/r5. : GOyrs, : : 14yr$. : 35yrs, Ans. £ (6) Thus suppose 40 200 20 10 T * r 1 20 Int. for 1 yr. < [«.6|00 Then as £10 14*. 8rf. : £201 5*. : : £40 : £750. Ans. £ s. And \l\2 6 4 years. Int. in 4 yrs. 9 4 3 7 8 Int. for 8 mo. \ pj^ ^ Whole int. 10 14 8 •^ < (7) Thus, suppose the cistern to hold 100 gallons. i Then 100-^ 45min.=2^^aL=ihe quantity which the' first cock discharges in a minute. And W0-^55min.=^l^jgal, the quantity which the second cock discharges in Imin. Then 100-^30mm.=3^^a/.=the quantity which the discharging cock discharges in Imin. Consequent- ly, 2^gaL^l-fjgaL=4^^gaL the quantity which the cistern receives by both the first and second cocks in a minute. Then as 2igals, run out in the same time, ^r^gctl. — S^a/.^jfg-aZ. that the cistern gains in Iwim. Then l^gaL : lOOgaL : : 1mm. : 2^^^, 21nii7i. 25 f see. Ans. DOUBLE POSITIO.V. (2) First suppose they received 276 3)552 184=:what A. spoiU. -i-250 434=:what B. spent. —276 1 58 B. w^as in debt every 7 year. 1106=7 years' debt. —350 756 error too much. 136 POSITION. Again suppose the salary was 300 2 3)600 200=A. spent. J- 250 450 B. spent. •—300 B. was every year 1 50 in debt. 7 And in 7 years he was 1 050 in debt. --350 700 error too much. Then 756 X 300=226800 700X276=193200 Difference of errors 56)33600(^600 the salary, f 336 of which=400 A.'s share, then 00 400+250=650 B.'s share. Ans. (3) First suppose 30 working days. §30 — 10 that he forfeits. Tlcceivcs 20 27 50 7 50 error too little. 137 Again suppose 20 worldng days. Forfeits 15 Receives 5 27 50 22 50 error too little. Then 2250x30=67500 750X20=15000 Difference of errors 1500)52500(35 workino- days. 4500 7500 7500 Therefore 50 — 35=15 idle days. Aiis. $ (4) First suppose 10 cow6=160 And 10 oxen=240 40 calves=240 The whole 640 —320 320 error too much. Again suppose 8 cows==12S And 8 oxen=:192 And32calves=192 The whole 512 320 192 error too much. 138 rosiTio:N'. Then 320x8=2560 192X10=1920 DiiFerence of errors 12S)640{5cows boxen & ^Ocaltes. 640 Ans. (5) First suppose Again suppose Ft, Ft, No. 2=20 No. 2=30 10=1 i5=i 15 15 25=No. 3. 30=No. 3. 4-15 +15 40 45=No. 2. —20 —30 20 error too much. 15 error too mucli. Tiicn 20x30=000 15X20=300 Difference of errors 5)300 60=No. 2, then 60—15=45= — No. 3. And then we have No. 1=15, No. 2=60, and No. 3=35, which added together= 120/1. the length of tht; pole. Ans. rosiTiox. 139 (6) Thus first suppose the whole property to have been worth jS £ 396 Again suppose 432 198=1 216=; —40 —40 158= A. 's share. 176=A.'8 132=^ 144=1 + 12 + 12 144=B.'s share. 156=B.'3 —80 —80 60=C.'s share. 76=C.'s 144 156 ^58 176 366 sum. 408 sura. 396 432 30 error of defect. 24 error of defect. Then 432X30=12960 396X24= 9504 Difference of errors 6)3456 £576 Ans. £ Then 576-^2—40=248 A.'s share. 204-r-3-f 12=204 B.'s do. 204—80=124 C.'s do. £576 proof. 140 POSITION. (7) First supDOse each boy received 3 2 6 = share of each 3 woman. 18= share of each — man. And 19X3= 67 11X6= 66 7X18=126 249 172 19 4J^ 1 76 7 J- error of excess. j £ Again suppose each boy received 1 2 2 share of each woman. 3 6 share of each man. £ And 19X1=19 11X2=22 7X6=42 83 172 19 4J 1 09 19 4J. error of defect. 1 , , ^ J| INVOLUTION AKJ) EVOLUTION . 141 £, S. d. Now 89 19 4|X3=2G9 18 0] 76 7JXl= 76 7J 345 18 8i Which -—166 sum of errors=:=jG2 1*. 8c?. -|- =each boy's ehare, which X2=:JC4 35. 4|(/.4- =each woman's share, which X3=jei2 10^. OJd!.-f = each man's share. Ans. INVOLUTION, OR THE RAISING OF POWERS. EXAMPLES. (2) 14X14X14=:2744. Ans. (3) 2.8X2.8X2.8X2.8X2.8X2.8=:4S1. 890304. Ans. (4) .263X.263X.263=.013191447. Ans. (5) }XiXiX|XiXjXiXi=^7i^^. Ans. (6) 401x401x401x401—25850961601. Ans EVOLUTION, OR THE EXTRACT- ING OF ROOTS. SQUARE ROOT. EXAMPLES. (2) 39375655(6275 Ans. (3) 14C6.179010(38.5o. Ans. 36 9 122)337 68)586 244 644 1247)9356 765)4217 8729 3825 12545)62755 7705)39290 62725 38525 Rem. 30 Rem. 76510 142 SQUARE ROOT. 1 (4) ^6385163(9817 Ans 81 (^) .0001 324960(.01 151 Ans. 1 188)1538 1504 21)32 21 1961)3451 1961 225)1149 1125 19627)149063 137389 2301)2460 2301 Rem. 11674 Rem. 159 1 (6) 18.362147(4. 16 285 Ans. 82)236 164 848)7221 6784 8565)43747 42825 Rem. i : (^) 15^5=,!' •"- ^' a^iarc root is J. Ans. (8) 36)1?-=- whose square root is ^. Ans. SQUARE ROOT. 143 (9) 500)3200(v^64(.8 Ans. (10) 50x64-f 49=:3|4 9, 3000 64 -; Then 3249(V=7J. Ans. 2000 25 2000 107).749 749 And \/. 6 4f. 8 denominator. 64 (11) 30x100+25=30.23 (12) 1296(36 Ans. 3X3=9 Then 30.25(5.5=5-,%. Ans. 25 66)396 396 105)525 525 (.13) 169(13 Ans. (14) 3097600(1760ydf^.=lmi/€. 1 1 Ans. 23)69 27)209 69 189 346)2076 2076 00 b 144 SQUARE ROOT. (15) Thus 15X15=225 24X24=576 V^801(28.3ft.An«. 4 48)401 284 563)1700 1689 Rem. 11 (16) 212X212=44944/^. And 202/Rein. 4902992 (5) .378621 350(.723. Ans. 7X7X7=343 J Defec. div. & sq. of 2=14704)35621 ^4-420 = com. divisor =15124)30248 J Defec. div. & sq. of 3=1555209)5373350 ( -f 6480=com. divisor =1561689)4685067 Rem. 688283 (6) 46.295363543(3.590 Ans. 3X3X3=27 J Def. div. & sq. of 5=2725)19295 I 4-450=com. divisor=3 175) 15875 J Def. div. & sq. of 9=367581)3420363 J +9450 = com. di. t=377031)3396279 Defective divisor 1 2888 1 )24084543 ALLIGATION. 147 (7) Thus4)X«|5= .2007722 J Defec. divis. & S( ( -f 200=complete 5 Defec. div. and sq 14-8700 = com. di (8) Thus =23%> which reduced to a decii Then .200772200(.585 125 [nal= Ans. Ans. ju. of 8=7564)75772 divisor = 8764)701 12 .of 5=1009225)5660200 visor= 1017925)5089625 570575 Rem ;j/36.|«=V36.8666664-(3.32 3X3X3=27 5 Defec. I 4-270= div. & sqi =complete 1. of 3=2709)9866 divi. =2979)8937 5 Defec. 14-198: div. & sq. = com. div of 2=32i?704)929666 isor =328684)657368 Rem. 272298 ^9®9^ ALLIGATION. CASE 1. (2) Cwt, 2 a 4 7 13 $ cts. $ ds. t 25 =50 00 20 50 = 82 00 18 621=130 37^ g262 371 Then as Ans. newt. : UwL :•, $262 ^71^^. : $20 I8jd*. 148 ALLIGATION'. (2) Mean rate 50 CASE 2. =36 at 34 cts. ^ =60 at 42 cts. I . = 16 at 86 cts. f^^^' = 8 at 110 cts. J CASE 3. (2) Mean rate 92 Then 86 cts. 94 cts 18 at 105 cts '^ Ans. CASE 4. (2) Mean rate 145 Then as 80 : 50 80 : 15 80 : 15 32 32 32 80 sum. of difter. 20 at 130 cts, 6 at 160 cts 6 at 180 cts i:| Ans. ARITHMETICAL PROGRESSION. 149 AFJTHMETICAL PROGRESSION. CASE 1. EXAMPLES. (2) Thus 40—1=39 (3) 10—1=9 2 com. dif. 4 com. dif. 78 36 2= 1st term. +10=^lst term. 80 1st Ans. 46 last term. 2= let term. -flO 82 sum. 56 40 10 2)3280 2)560 gl6.40 Ans. 280 2d Ans. (4) 75—1=74 2 common difference. 148 -f 6= 1st term. ^ ^1.54 for the last* Ist Ans. 6= 1st term. 160 sum. 75 800 1120 2)12000 00 in the whole. Ane. ^ 2 150 ARITHMETICAL PKOGRESSION. CASE 2. (2) Thus 175 —21 8—1=7)154 . jj22 common difference. And 175+21=196 sum of extremes. 8 number of terms* 2)1568 784 whole sum. Lastly 21-1-22= 43=2d payment. 43+22= 65=3d 65+22= 87=4th 87+22=109=5th 09+22=131=6th 131 + 22=153=7th 153+22=175=8th 763 21= 1st payment. $784 proof. (3) Thus 49 Then 49+4=53 sum of extremes. -—4 10 number of terms. 10— .1=9)45 2)530 5com. dif. Received $2.65 Ans. GEOMETRICAL TROGRESSION. 151 GEOMETRICAL PROGRESSION. EXAMPLES. (2) Thus power 12 3 4 Ratio 3 9 27 81 27 3d power "567 162 2187=7th power. 5= 1st term. l6t Ans. 10935=:last term. 3 ratio. 32805 — 5= 1st term. Ratio less 1=2)32800 jei6400 Ans. 2nd (3) Thus power 1234567 8 9 Ratio 2 4 8 16 32 64 128 256 512 512 1024 512 * 2560 262 144= 18th p. 4=2d do. 1048576=20th p. 1 1st term. 1048576=lastt. 2 ratio. 2097152 l = lstt. Ratio less 1= 1)2097151 Ans. g20971.51c LA.LS. COMPOUND INTEREST BY DECIMALS. EXAMPLES. (2) Thus, tabular number 1.2155062 750 607753100 85085434 911.6296500 Amourtt of £1 for 6mo. 1.024695 from table first. 45581482500 82046668500 5469777^000 36465186000 18232593000 91162965000 je934. 1423442067500 20 «.2.8468841350000 12 rf. 10. 1626096200000 £ 8, d. Amount 934 2 10-}- Principal 750 Interest 184 2 10+ Ans. ANNUITIES AT COMPOUND INTEREST. 1 53 CASE 2. (1) Thus £695 13*. 9d.=:695.6875£. Then from tab. II. 1.2762815)695.68750(545je. 1*. 9rf.-f Ans. (2) ThusjeseO 5«. 3». DUODECIMALS. ADDITION OF DUODECIMALS. EXAMPLES. Ft, (1) 10 15 18 12 in. " '" "" Ft, in, " 5 6 11 6 (2) 37 8 10 9 5 2 10 43 11 2 4 17 9 19 7 5 8 6 5 7 18 4 1 /// ffff 6 9 4 7 3 8 7 2 Ans. 57 3 8 3 8 Ans. 119 7 7 10 2 1 156 DUODECIMALS. Ft. in. " (3) 16 8 14 6 17 9 2 Ans. 48 11 2 SUBTRACTION OF DUODECIMALS. EXAMPLES. Ft, in. " '" "" Ft. in. " '" "" (1) From 38 8 4 7 5 (2) From 720 3 8 1 6 Take 15 11 6 9 3 Take 13 9 4 7 10 Ans. 22 8 10 2 2 Ans. 706 6 3 5 8 Ft. in. " '" "" (3) From 475 7 2 Take 81 2 5 10 6 (2) Ans. 394 4 8 16 MULTIPLICATION OF DUODECIMALS. CASE 1. EXAMPLES. Ft. in. 64 10 5 7 Ft. in. " (3) 6 9 3 3 5 31 11 10 274 2 2 9 10 3 20 3 9 306 1 JO Ans. 23 1 7 3 (2) (3) sq. 6 1 - 4"- 1 DUODECIMALS. 167 CASE 2. Ft, in, " \ 81 10 4 7X2=14 573 4 2- 1146 8 J 40 11 2 L 6 9 10 4 » 2 3 3 5 4 6 9 10 4 1)1196 7 9 7 8 is,l22 8 7 9 7 8 Ans. in, 4 1 3" 6//' 1 1 I 7 ^t. in. " '" . 2 5 7 2 } 9 10 4 8 2 5 7 2 7 4 9 6 12 9 7 9 10 4 8 2 5 7 2 ft. 1 110 8 5 4 11 10 contents of Ish. 10X10X10=1000 10 10 7 6 1 10 4 10 108 9 10 5 1 6 7 4 10 1088 2 8 3 3 6 14 Ans. 158 PROMISCUOUS EXAMPLES. PROMISCUOUS EXAMPLES. (1) Thus A.'s 25 years. + 15 B.'s 40 years. + 12 C.*s 52 years. Ans. % Cl8, % Cts, (2) Thus 220 50-f-5=44 10 A.'s own share. 220 50+6=36 75 B.'s do. 80 85 sura. 220 60 139 65=C.'s own share. ^ ds. j5 ds.m. Then 36 75+2=18 37 5=^ B.'s share. 44 10 62 47 5=A.'s last share. ^ els, m. And 18 37 5 139 65 Ans. 158 02 5=C.'s last share. PROMISCUOUS EXAMPLES. 159 (3) glcrO— g7l : poo : : p6 25cts, : g60 Slds. 5m. -1-25. For 5625X100=562500 the dividend. And 100—71=921 the divisor. Then 562500— 92i=g60 Slots. 5?n.-f 25. Ans. (4) Thus B. gains 2 miles per hour. Then as 2m. : 50m. : : Ihr, : 25hrs. 1st Ans. Now as B. went at the rate of 10 miles per hour for 25 hours, 10x25=250 miles, the 2d Ans. (5) Thus^=J)750 187 50 whole price of the damaged. 100 loss. 87 50 what it sold for. Then $1 25cts, : g87 50c^^. : : 1yd, : lOyds.zzzqmn- tity damaged. And 70 X 4=2S0yds, the whole quantity. 70 210 undamaged. And ^750 OOd*. cost. 87 50 received for the damaged. 2l0yds, : $662 50 : : 1 : g3 I5lcts.+ Ans. 160 PKOMISCUOUSf EXAMPLES.. (6) Thus lOGO— 1=:=999 number of terras— 1. ♦ 1 ft. common dilTerence. 999 2 ft., first term. 1001 last term. 2 1003 sum of the terms. 1000 2)1003000 3)501500 ft. 220)167166+2 ft. 0)759+186 yds. 94+7/wy. UQyds. 2ft. Ans. (7) Thus admit the wall to contain 3600 feet. Then 20)3600(180 feet raised in a day by A. B. & C. 24)3600(150 * B. C. &D. 30)3600(120 C. D.& A. 36)3600(100 A. B. & D. 3)550 1 83i feet per day by altogether. Then 183 J- And 183.} B. C..& D. 150 C. D. & A. 120 A. 33} PROMISCUOUS EXAMPLES. 161 And 183 A. B. &D. 100 C. "83^ ^ And 183 J A. B. & C. 180' D. days. Then, feet per day by A. 33J)3600(108 for A. to do it in. do. by B. 63fj3600(56|J B. do. do. by C. 831)3600(43]. C. do. do. byD. 31)3600(1080 D. do. And 1831)3600(19^ days all working together. Ans. d, d, (8) Thus 4 crowns at 146 each=584 3 dolls. 2 ducats 108 136 1180c;. sum. And £1055 155.=253380cif. Then 1180 : 253380 d. 584 324 272 d, d. 125402-rl46=:858f|cr. 69572 " 58406 2-rl46=:858f|cr. ) 2-T-108=644^5^g. \ 6-M36=429||<£wc. ^ Ans. (9) Thus 9wi. : 21m. : : g332 50c<5. : $775 83jc«5. Ans. For 33250X21=698250 the dividend. And 9=the divisor. Then 698250^9=^775 ^^Ids. O % 162 PROMISCUOUS EXAMPLES. (10) Thus 12 4 16yrs.=10.n3'711 Table IV. Time of reversion 12 = 8.86325 do. 1.97462 difference. 720.25 annuity. 987260 394904 3949040 1382164 gl422. 1480300 Or ^1422 14cls,' 8m.+ Ans. (11) 3150 gigs — 2250 X Sets, igs~7X 5=^ g cts, ) wagons wh. > 135 00 for the wagons. cts.= 3 3150 gigs -f- 3 X 5=^ 5250 footmen wh. > 52 50 for footmen. X let.— ) 6250 footmen -r- 6 X 4 ^ = 3500 horsemen > 70 00 for horsemen, which X 2ds*= y 3150 gjs at 4cts. per ) j^g ^^ ^^^ ^j^^ Amount of, toll 383 60 Ans. (12) Thus 15^a/5. in 3min.~5gals. per min. that nm in. And 20-7-5= l/.:flf7*. that run out in a min. Con- sequently, the gain is 5 — 4=^gaL per min. which is OOgnh. per hour. Then nO-'60=50^<»vTA?. yet to nm in. Then Sgals, : SOgals, : : Imwi. : 107nm. Ans. PROMISCUOUS EXAMPLES. 163 (13) Thus 264 6 6 3 1 15 84 Int. for 1 year. 7 92 3 96 1 1 88 Int. for 9 months. 264 00 30 00 profit. g305 88 for the whole. lbs ^ cts Wl Then 28cw?*.=3136)30588(0 9 7+ Ans. 28224 23640 21952 Rem. 1688 (14) Thus, the proportions are A. 4 B. 5 C. 3=12. Then 12 : 780 ' 4 : 260 A.'s share of profit 5 : 325 B.'s do. ' 3 : 195 C.'s , do. 1st Ans. pSO proof. $ mo. Then 260x5=1300 325X7=2275 195X9=1755 5330 164 PROMISCUOUS EXAMPLES. r 1300 : 1405 36 A. 's stock. Again 5330 ; 5762 : : \ 2275 : 2459 39 B.'s ( 1755 : 1897 25 C's g5762 00 proof. Now 2459 39 2087 00 B. received. 372 39 B.'s loss of stock. And 325 00 do. of gain. Ans. '^697 39 A. & C. would gain. (15) 1004-51=105 75. $ cts.m. Then 105 75 : 100 : : 1000 : 945 62 6 cost C. 20 75 less. $924 87 6 cost B. Again 100 —5 50 94 50 : 100 : : g924 Slds, 6m, : g978 llOcts. 4m. that the whole cost A. which ~20AM^.=g48 93c^*. 5m. -f Tperhhd. Ans. (16) 10X11=110 sold for. 10 X 7= 70 worth. $40 gain of A. $ ds, m. $ ctt. And 110-r3= 36 66 6+ paid cash. 5 25 110 00 4 50 $73 33 3 to pay in paper. $0 75 B. gains. 1 Then 450 : 75 : : 73 33 3 : $12 22ds. 2m. gain of 1 B. $40— $12.22.2=r$^27.77.8. Ans. PROMISCUOUS EXAMPLES. 165 (17) Thus 21—14=7 years to be of age. Then gl 300 6 ' 7800 int. first year. 1300 1273 amount— 100. 6 7668 int. second year. 1278 125468 amount— 100. •6 752808 intnhird year. 125468 12299608 amount— 100. 6 73797648 int. fourth year. 12299608 12037584 amount— 100. 6 72225504 int. fifth year. 12037584 11759839 amount— 100. 6 70559034 int. sixth year. 11759839 11465429 amount— 100. 6 68792574 int. seventh year. 11465429 ^ i 1 15.33.54m. amount— 100. Ans. IGG PROMISCUOUS EXAMPLES. Another solution : First, 1.067=1.5036302. See table II. Arithmetic. And 1.5036302X1300=1954.719. Amount at . Com- pound Interest. Also, 8.393837X100=839.383. Amount of glOO An- nuity for 7 years, table III. Hence S5l954.719—g839.383==glll5 23cts. 5m. Ans. (18) E B F 64 ^K ^'^""— — ^ 14 D 50 C 76~^ L Statue, L Thus, referring to the above figure. A B is a perpendicular line erected on the centre of the statue's base, which forms the side A C of the right angle A C D ; and the other two sides, A D 86 and C D 76 are given to find the length of the side A C. Now 76^=5776 & 862=7396 —5776 x/1620diff. (40.2-L = AC PROMISCUOUS EXAMPLES. 167 Then 40.2-|-14 the difference between the columns =54.2 the whole length of A B. Then 54.22= 2937.64 & 972= that is A E=9409 —2937.64 V6471.36=(80.44-f for E B. + 76 that is BF 14=DF 156.44=EBF 14 156.44 56 62676 14 62576 93864 196 78220 15644 24473.4736 196 2^/^24669.4736=157 ft. Ans. Note. — ^This solution snpposes the statue to be lower than the columns : admitting it to be higher, the operation will, of course, be different; but may readily be performed from the one here given. (19) Isec. : 47*ec. : : 1150/?. : 54050/?. Ans. (20) 15m. 7/5/^=83820/?. Then 1150/?. : 8382t)/?. :: Iscc, : Im. I2{^pec, Ans. 168 PROMISCUOUS EXAMPLES. (21) First suppose J of 8.2245 in. to be gold. 4.1 1225=^ 4. 1 1225 in. of sil. 10.36 5.85 2467350 1233675 4112250 2056125 3289800 2056125 42.6029100oz.g. 24.0566 625o5r. sil. 24.0566625 66.6595725 63 3.6595725 error of excess. Again suppose | of 8.2245 in. to be gold, the rest silver. 2.7415=^- 10.36 5.4830=silver. 6.85 164490 82245 274150 28.401 940o2r. 32.075550 60.477490 63. 274150 438640 274150 32.075550oar. sil. 2. 5225 1 error of defect. [Seefolloiping page< PROMISCUOUS 1&XAMPX.ES. 169 in o o Tt o «> 00 1— GO 1.^ O GO d d to LO vn ^ l> 1— ' o ^ 5 (^ lo X UO c^* 1?^ o CD r- ^ <-> to UO (M 05 G^ CO O G^ CO in CO GO ©< II fl lO .Q^T3 (^ ^ !=! t- o o O O O o o o O 10 LO O LO CO Oi LO O LO G^ G>^ GO C5 CO o O CO ^ G-f ^ G^ 05 ""^ -rf s^^ t- LO CO CO CO O t- G^ Oi GO <3^ 'f O UO O ^ >0 Tf CO ©^ GO ■^ a> CO GO 5< CO CO O 05 Oi "^ LO "<* Lf5 LO CO CO r-i r-* 0) ^ •M ns C KJ m < Cf^ o M r/: a> O) > o -73 s-j (C C3 o M a^ en o GO o Tj* Eh< GO o -3 o o CO CO 170 PROMISCUOUS EXAMPLES. Another solution : oz. oz. oz. First 63-^8.2245=7.66 weight of a cubic incli of the mixture. Til "7 ftA 5 10.36s^r=1.81 proportional hulk of gold, inen 7.t)t) ^ 5,85^=2.7 proportional huJk of silver. Also 1.81X10.36±=18.7516 proportional trei^^,« of gold. And 2.7 X 6.85=15.795 proportional lOCTg*^ of silver. 34.5466 sum. oz. Hence 34.5466 : 18.7516 : : 63 : 34.19587 gold ) > And 34.5466 : 15.795 : : 63 : 28.80356 silver. ^ " Proof 62.99943 (22) Thus llhs, beef at 5jcf5.=40}cfe. 5 bread at 6 =30 Then AO\cts, : g34 50cts. : : 30cf^. : $25 lids. 4wi.+ Ans. (23) Thus^oflof JJf=^V Then l^/^«^=fif||. Ans, (24) 1000 6 60|00 int. for 1 year. 8 int. for 8 years. PROMISCUOUS EXAMPLES. 171 Then 8 years. 6 per cent. 48 100 148 amt. of JJlOO for 8 yrs. at 5 per cent $ $ $ $ c«*-"»- Then 148 : 100 : ; 1000 ; 675 67 5 the present worth. 1000 00 g324 32 5 discount. 480 00 interest. Ans. gi55 67 5 difference. (25) V32=p5.656-|- v^24=4.9 10.556 sum. V67 =4.06+ Ans. 6.496 difference. (26) Thus glOO : ^105| : : $24.30 : ^2587 20cf*. Ans. (27) Thus the amount of gsOO lods, for 9 months at 6 per cent.=::g533 2nds. 4m. 172 PROMISCUOUS EXAMPLES. cts, ^ CU. And 5064x21=126 60 price of the boards. 140X13= 10 20 do. tallow. 144 80 amt. 623 28 4 §378 48 4 to receive in flayseed. Then as ^Z\cts.: §378 48c«#. 4m. : : Ihu, : 409j|J6w. Ans. (28) 9 yrs.=36 qrs. the sum of terms. —1 35 3 common difference. 105 -f 6=lst term. Ill last term. 6= let term. 117 sum. X 36 number of termi. 702 351 2)4212 g21.06cf*. duehim. Ans. PKOMISCUOUS EXAMPLES. 173 (29) Thus Syrs, — 2\yrs.:=^2lyrs, Then 1.06x1.06x1.045=1.174162 divisor. And 2363.3875 — 1.174162 = ^2012 ^2cts, ^m, Ans. (30) Thus, from January 14th, 1802, till July 5th, 1807, inclusive=5 years 173 days. And the amount of jjl 854.69 for that time at 5 per cent per annum = ^2362.3161 285. paid off. 2077.3161 second bond. 4| 83092644 10386580 5193290 98.67.2514 int. of the 2d bond for 1 yr. Then 98672514 : 365 : : 52.65 : 194 days the time of the second bond. Now 2077.3161 52.65 interest. 2129.9661 amount. 102.43 paid off. 2027.5361 3d bond. !>£> 174 PROMISCUOUS EXAMrLES. Which was out from J«nnary 12, 1808, till Octo- ber 26th, 1813, whiuh L^ 5.789 years. $9Aj7.0M3 last amount. 20'27.5361 last bond. 469.4962 gained on the last bond, '' — which was out 5.789. years, and this bond inclusive to the time = 11737.4064829. Then 11737.4064829 : 469.4962 ; : 100 : 4 per cent. Ans. (31) First suppose 10 horses at 50=500 20 cows 20=400 60 sheep 4=240 51110 sum. 45 684 error of excess. 3 $ Agam suppose 8 horses at 50=400 16 cows 20=320 ' 48- sheep 4= 1 92 g912 sura. 456 456 error of excess. PROmSCUOUS EXAMPLES. 175 Then 684 x 8=:5472 456X10=^4560 Difference of errors=228)9 12(4 horses. 912 $ $ For 4 horses at 50—200 ) Scows 20=160 >Ans. 24 sheep 4= 96 ) 55456 proof. Another solution: $ First 50 price of each horse. 20x2=40 price of cows for each horse. 4x 6=24 price of sheep for each hbrse 114)456(4 numher of horses. . 456 $ $ Then 4 horses at 50=200 4X2= Scows 20=160 And 8x3=24 sheep 4= 96 456 proof. 176 PEOMISCUOUS EXAMPLES. (32) Thus r 16--V = 6 Mean rate 19 ? 17>, ) = 5 3+2=5 oz, oz, mi r in ^5 : 10 of 17 carats fine. ) .^^ Then as 5 : 10 : : J 5 ^ ^0 ^^ 24 carats fine. \ ^''^' (33) £100 : jei20 : : £230 5*. : £276 6*. the amount in sterling. Then as £l : £276 65. : : J4 44c««. 4m. : gl227 filets. 7wi.4- Ans. (34) Thus f^'ff+J=l4|, and ||| subtracted from 1= ^|^=the 27 feet. Then if| : nft. : : 1 : 113/55. 4m. Ans. (35) $1 : 56jc?5. : : $400 : $32 14fd5. AnS. (36) Thus 30 +96 126 sum. 25 number of terms. 630 252 2)3150 $15.75 Ans. BOMISCUOUS EXAMPLES. 177| (37) Thus 4 : 9 t : 47 : 105.75 the greater number. 47 152.75 sum. 58.75 differ ence. 76375 106925 122200 76375 Product 8974.0625 Ans. TBS CND. v> ^f^ '->/ ^^