SB E73 bfil ITHMITIC TE SERIES LIBRARY OF THK UNIVERSITY OF CALIFORNIA. & Received ^PtO^T , 189$. Accession No. w *?*/$?) . Class No. J%tyyn A 735- Sample Book PROPERTY OF THE HlCKS=JUDD Co. 23 FIRST STREET SAN FRANCISCO KEY ADVANCED ARITHMETIC (California State Series) S Containing full solutions to all of the Examples WITH AN APPENDIX Containing the answers to Fifteen Hundred Examples in the PRIMARY NUMBER LESSONS PREPARED BY PROF. A. M. ARMSTRONG, PH. B. Principal of the Colusa Commercial and Normal Institute and Author of the California Teachers' Examiner SAN FRANCISCO THE BANCROFT COMPANY Copyright, 1888 BY THE BANCROFT COMPANY Generally speaking, rules a,re omitted from the State Series of Arithmetics, and consequently a demand for a guiding "KEY" has arisen. This book is published to supply that want. The author does not claim that his methods are in aU cases the shortest and the best. With few exceptions, they are the ones naturally followed by his students, and it is his belief that as a rule they represent the solutions that will be used by the average pupil that has been taught "to look for a reason for everything " The book is open to criticism, and correspondence is invited in order that succeeding editions may contain such alterations as will make the Key truly representative of the arithmetical work of California teachers. A. M. A. Colusa, Cal., June 188S. KEY TO CALIFORNIA ADVANCED ARITHMETIC PART I. INTEGRAL NUMBERS PRACTICAL ADDITION AND SUBTRACTION 47. Page 28. 1 4750 -1287 = 3463 A. 2 156 + 273 + 195 + 390 + 312 = 1326 trees 3 83 +147 = $230 4 263-197 = 66 miles 5 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 = 365 d'ys 6 2500 + 350 + 65 + 119 + 47 = $3081 7 21,420 -16,283 = 5137 people 8 1885 -1822 =63 years 9 3047 - 2816 = 231 miles Mo. 10 4617 + 3943 + 3248 + 24,257 + 3308 = 39,373 votes (i) 2 PRACTICAL ADDITION AND SUBTRACTION 11 4617 + 3943 + 3248 + 3308 = 15,116; 24,257-15,116 = 9141 12 187 + 298 =$485 drew; 2375 -485 = $1890 rem. 13 16,120+ 75,025 = 91,145 both; 75,025 -16,120= 58,905 Chiuese 14 187 + 153 = 340; 425 - 340= 85 trees 15 212 -185 = $27 16 1799-1732 = 67; 1865-1809 = 56; 67-56=11 years, Wash. 17 1276+125 = 1401; 1276 + 1401 + 375 = 3052; 1276+1401 + 3052= 5729 Cen. All 18 1852-70=1782 19 1483 + 578 + 230+1020 = 3311 20 145 + 65 = $210 21 Present year - 1850 = A ns. 22 309 + 576 =885 sum; 576 -309 = 267 Diff; 885-267 = 618 23 2375 + 450 = $2825 ; 31 00 - 2825 = $275 gain 24 602 + 1312 + 490 = 2404 to Chicago ; 2404 + 963 = 3367 to N. Y. 25 602 + 1312=1914; 490 + 963=1453. 1914-1453 = 461 miles 26 Present year - 1492 = Ans. 27 89,225 + 102,406 + 2960 + 2010 + 356=196,957 votes 28 102,406 - 89,225 = 13,181 votes 29 89,225 + 2,960 + 2010 + 356= 94,551 ; 102,406 - 94,551 = 7855 30 17 + 26 + 8 + 18 +11 + 7 = $87; $100 -$87 = $13 change 31 173 + 49=222 32 1208-749 = 459 33 970-127 = 843 34 800 + 925 + 1175 = $2900; $4000 -$2900 =$1100 35 100-23=77 36 1728-209=1519 PRACTICAL ADDITION AND SUBTRACTION > 37 Present Year - 69 = Ans. 38 1922 -birth yzar=Ans. 39 2500 + 1550+1325 + 725 = $6100 40 57 + 73 + 61 + 93 + 84+101 + 112=581 pupils 41 581 -273 =308 girls 42 1706 + 84=1790 A. D. 43 50,267,519 - 38,567,617 = 11,699,902. gain 44 6608 + 11,591 = 18,199 mi.; 11,591- 6608 = 4983 miles more 45 31 + 28 + 31 + 30 + 31 + 30 = 181days 46 145 + 25 = 170cts.; 145-25 = 120 cts.; 170-120=50 cts. 47 2783-1296 = 11487 48 125 + 125 + 125 = $375 ; $375 - $171 = $204 saved 49 370 + 370 + 370 + 370 = $1480 saved 50 1250 + 498 +726 = 2474 cen.; 550 + 1500=2050 cen sold; 2474 -2050 = 424 cen. rem. 51 753 + present year Ans> 52 4004 - 1652 = 2352 B.C. 53 29,062 - 14900 = 14162 feet 54 175 + 213 +94 =482 miles 55 190 -45 = $145 cost 56 125 + 256+ 114= $495 spent; 1000 - 495 = $505 left 57 130 + 115 + 58 = 303 sheep; 325 + 345 + 203 = $873 58 2375 + 250= $2625; 2625 -175 = $2450 59 $3400+ 1700+ 1700 + 1500 + 1500+ 1500^ $11300 60 2114 - 906 = 1208 drunks 61 31 + 30+31 + 30 + 31 = 153 days 62 1571 -753 = 818 years 4 PRACTICAL ADDITION AND SUBTRACTION 63 $2700 -$725 =$1975 64 30+31 + 31 + 30=122 days; 31 + 28 + 31 + 30 = 120 days; 122 -120= 2 days 65 1769 + 79=1848 A. D. 66 29,062 + 1317=30379 feet 67 175-30=145cts.; 145-30= 115 cts. 68 32 + 32 +32 + 32 = 128 trees; 128 -72 =66 lemon tree* 65 Page 41 1 25 x $37 =$925 2 32x24 hrs. = 768 hrs. 3 11 x $16= $176 4 18x5280 ft. = 95 ,040 ft. 5 24 x 23 miles = 552 miles 6 93 x 104 trees = 9672 trees 7 35x $33,275 = $1,164,625 8 960 X $75 = $72,000 9 346 x 65 lbs. = 22,490 Ibs. 10 12 x $75 = $900 11 24 x $23 =$552 12 26x19 =$494 13 ]2x $525 =$6300 81 Page 54 1 925-^37 = 25 cows 2 744-i-24 =31 days 3 176-r 10= 11 months 4 552-1-23=24 hrs. 5 9672-5-104= 93 acres 6 l,164,625-j-33,275 = 35mi. 7 72,000-J- 75 = 960 acres 8 22,490-7-65= 346 chests 9 9004- 75 = 12 months 10 605^55 = 11 ponies PRACTICAL MULTIPLICATION AND DIVISION 5 PRACTICAL MULTIPLICATION AND DIVISION 82 Page 1 50x45 yds. = 2250 yds. 2 1728-i-8 = 216 T. 3 190 x $112= $21,280 4 15x320 =4800 rods 5 llx$31 = $341cost 6 W 1500-7-14=107 T., $2 rem. 7 15x235=35251bs. 8 19,6; 19 108 = 2, 2, 3, 3, 3 252 = 2, 2, 37-3, 7 2x2x3x3 = 36G. C. D. * 20 39 = 3, 13 52=2, 2, 13 65 = 5, 13 13 G. C. D. 21 84 = 2, 2, 3, 7 132 = 2, 2, 3, 11 2x2x3=12 G. C. D. 22 168=2, 2, 2, 3, 7 539 = 7, 7, 11 7 G. C. D. 23 112=2, 2, 2, 2, 7 147 = 3, 7, 7 168 = 2, 2, 2, 3, 7 7 G. C. D. 24 287 = 7, 41 369 = 3, 3, 41 41 G. C. D. 25 55 = 5, 11 110=2, 5, 11 5x11 = 55 G. C. D 26 81 = 3, 3, 3, 3 120 = 2, 2, 2, 3, 5 141 = 3, 47 3 G. C. D. 27 78= 2, 3, 13 169 = 13, 13 130= 2, 5, 13 13 G. C. D. 28 150 = 10, 3, 5 210=10, 3, 7 330 = 10, 3, 11 10x3 = 30 G.C.D. 29 99 = 3, 3, 11 132=2, 2, 3, 11 3x11 = 33 G. C. D. 30 120=2, 2, 2, 3, 5 165 = 3, 5, 11 3x5 = 15 G. C. D. 31 120 = 2, 2, 2, 3, 5 252 = 2, 2, 3, 3, 7 2x2x3 = 12 G. C. D. 32 85 = 5, 17 102=2, 3, 17 17 G. C. D GREATEST COMMON DIVISOR 11 33 42=2, 3, 7 77 = 7, 11, 91 = 7, 13 7"G. C. D. 34 34=2, 17 44=2, 2, 11 2G. C.D. 35 28=2, 2, 7 98=2, 7, 7 2x7 = 14 G. C. D. 36 110 = 10, 11 210 = 10, 3, 7 10 G. C. D. 88 Page 66 1 135 = 3, 3, 3, 5 270 = 2, 3, 3, 3, 5 3x3x3x5 = 135G. C. D. 2 207 = 3, 3, 23 1017 = 3, 3, 113 3x3 = 9 G. C.D. 3 702=2, 3, 3, 3, 13 4706 = 2, 13, 181 2x 13 = 26 G. C. D. 4 3003= 3, 7, 11, 13 11,011 = 11, 7, 11, 13 7x11x13=1001 G. 0. D. 5 725 = 5, 5, 29 4350=2, 3, 5, 5, 29 5 x5x 29 = 725 G. C. D. 6 87 = 3, 29 203=7, 29 29 G. C. D. 7 750=2, 3, 5, 5, 5 129 = 3, 43 3 G. C. D. 8 597 = 3, 199 237 = 3, 79 3 G. C. D. 9 975 = 3, 5, 5, 13 555 = 3, 5, 37 3x5 = 15 G. C. D. 10 510 = 2, 3, 5, 17 714=2, 3, 7, 17 2x3x17 = 102 G. C. D. 11 378=2, 3, 3, 3, 7 1818 = 2, 3, 3, 101 2x3x3=18 G. C. D. 12 1011=3, 337 1101 = 3, 367 3 G. C. D. 12 GREATEST COMMON DIVISOR 13 246=2, 3, 41 438 = 2, 3, 73 2x3 = 6 G. C. D. 14 720=2,2,2,2,3,3,5 256=2, 2, 2, 2, 2, 2, 2, 2 2x2x2x2=16G. C. D. 15 981 = 3, 3, 109 711 = 3, 3, 79 3x3 = 9 G. C. D. 16 846 = 2, 3, 3, 47 329 = 7, 47 47 G: C. D. 17 279 = 3, 3, 31 496 = 2, 2, 2, 2, 31 31 G. C. D. 18 213 = 3, 71 284=2, 2, 71 71 G. C. D 135 = 3, 3, 3, 5 270=2, 3, 3, 3, 5 207 = 3, 3, 23 1017 = 3, 3, 113 3x3 = 9 G. C. D. b 702= 2, 3, 3, 3, 13 4706= 2, 13, 181 3003= 3, 7, 11, 13 11011=11, 7, 11, 13 13 G. C. D C 725=5, 5, 29 4350 = 2, 3, 5, 5, 29 87=3, 29 203 = 7, 29 29 G. C. D. d 750=3, 2, 5, 5, 5 129 = 3, 43 597 = 3, 199 237 = 3, 79 3 G. C. D. c 975 = 3, 5, 5/13 555 = 3, 5, 37 510=2, 3, 5, 17 714 = 2, 3, 7, 17 3 G C. D f 378=2, 3, 3, 3, 7 1818=2, 3, 3, 101 1011 = 3, 337 1101 = 3, 367 3 G. C. D GREATEST COMMON DIVISOR 13 g 246=2,3, 4 438 = 2, 3, 73 720=2,2, 2,2, 3,3,5 256 = 2,2, 2,2,2,2,2,2 2 G. C. D. h 981 = 3, 3, 109 711 = 3, 3, 79 846 = 2, 3, 3, 47 329 = 7, 47 No C. D. 89 Page 67 539(168 504 (3 168(35 140 (4 _ 28 (1 28 (7 G.C. D. 28 (4 168(147 147 (1 147(21 G.C.D 147 (7 369(287 287 (1 287(82 246 (3 82(41 G. C. D. 82 (2 169(78 156 (2 78(13 G.C.P. 78 (6 636(371 371 (1 371(265 265 (1 265(106 212 (2 106(53 G. C. D. 106 (2 961(279 837 (3 279(124 248 (2 124(31 G. C. D. 124 (4 14 LEAST COMMON MULTIPLE LEAST COMMON MULTIPLE 90 Paga68 1 5 3 3 2 30 45 90 6 9 18 236 2 2x3 = 90 ( 24 36 42 6 7 2 3 7 = 504 3 2 4 8 10 5 2455 255 = 40 4 5 5 3 2 2 3 2 5 12 15 30 12 3 6 4 2 7 2 12 18 24 7 6 9 12 7 2 3 4 :60 7 3 2=504 6 5x5 | 75 100 3 4=300 7 2x5 20 30 40 3 2=120 8 11 9 5 3 " 33 44 21 3 4 7 = 924 105 120 21 24 * 10 3 3 2 11 7 3 12 3 2 7 8 = 840 18_j_27 12 694 234 3 2=108 14 21 15 2 3 15 2 5=210 3 4 5 6 10 4 5 2 10 5 25 5 13 2x3 2 3 2 14 2x2 3 2 2 =60 12 18 24 36 72 2 3 4 6 12 3236 2 2 = 72 12 16 20 24 3456 452 2 5 =240 LEAST COMMON MULTIPLE 15 15 7 2 16 5x 17 2 3 18 3 2 2 2 5 19 2,: 20 7 21 2, 22 3 5 23 2 3 7 28 2 35 24 2, 5 120 140 210 4 6 5 7 12 14 21 2 3 5 = 420 5 | 50 75 125 2 12 23 3 6 3 2 =840 25 5 15 21 35 9 2 3 5 = 750 10 12 3 3 21 7 9 5 6 7 7 7 3 24 5 2-180 30 36 40 26 10 | 38 = 105 57 95 8 10 12 40 2 27 3,3 18 3pr K7A 4 5 6 20 O D/U 27 36 o 5 3 10 535 i, 3 3 |7 3 =360 108 132 144 2 2 3 4 28 13 1 26 3 2 = 103 39 65 9 1 12 3 11 4=4752 11 14 21 2 29 11 33 3 5 = 390 44 55 2,3 175 11 2 3=462 I 72 84 132 3 4 5 = 660 30 12 1 84 96 7 8=672 31 12 13=156 32 13 16 = 208 33 5 1 23 25 30 6 7 11 = 5544 105 120 |25 35 40 5 7 8 = 4200 30 42 126 15 21 63 5 7 21 23 5 6 = 3450 5 3=630 16 LEAST COMMON MULTIPLE 34 9 11 = 99 35 2} 24 26 12 13=312 36 24 25 = 600 37 2.2 | 64 84 16 21 = 1344 38 2 \ 34 36 17 18=612 39 2.3 1 17 18 30 17 3 5 = 1530 92 Page 69 1 189(105 21)105 105 (1 "5x189=945 84=2, 2, 21 2 169(91_ _ 91(1 7x169=1183 78 = 2, 3, 13 3 169(78_ 13)78 156(2 6x169 = 1014 13 8 279(124 31)124 248 (2 4x279 = 1116 31 9 21(15_ 3)15_ 15_(1 5x21 = 105 6=2, 3 10 28(21_ 7)21_ _2J_ (2 3x28=84 7 11 20(16 4)16 4 132x119=15708 16 (1 Tx~20=80 4 5 539(168 7)168 504 (3 24x539 = 12 45(40 5)40 35 = 5x7 12936 40 (1 8x45 = 360 5 6 369(287 41)287 287 (1 7x369= 82=2x41 2583 13 45(36 36 (I 9)36 4x45= 9 180 7 168(147 21)147 14 54(36 18)36 147 (1 7x168= 36 ~U~ 2x54= 21 1176 18 108 LEAST COMMON MULTIPLE 17 15 32 16=32 16 81(63_ 9)63_ 63(1 7x81 = 567 18=2, 9 17 64(56^ 56 (1 8 18 44(33 33 (1 11 8)56 7x64=448 11)33 3x44=132 19 1017(207 9)207 828 (4 23x1017= 189 = 3, 3, 3, 7 23391 20 11011(3003 9009 (3 2002=2,1001 1001)3003 3x11011 = 33033 21 203(81 29)87_ 174(2 3x203=609 29 22 750(129 3)129 645 (5 43x750= 105 = 3,3,3,5 32250 23 1818(378 18)378 1512 (4 21x1818 = 306=3, 3, 2, 17 38178 24 981(711^ 9)711 711(1 79x981 = 270=10,3,3,3 77499 25 846(329_ 47)329 658(2 7x846= 188=2,2,47 5922 PRACTICAL FACTORING. 94 Page 70 1 15=3, 5 18=3, 3, 2 3 G. C. D. 2 120=2, 2, 2, 3, 5 128=2, 2, 2, 2, 2, 2, 2 144=2, 2, 2, 2, 3, 3 2, 2, 2 = 8 ft. 3 3, 4, 5 =60 miles. 4 360=5, 2, 3, 3, 4 480=5, 2, 3, 4, 4 5, 2, 3, 4=120 ft. 360+480=840-M20=71. 5 5 1 20 15 4 3 = 60min. 60-M 5 = 4 x 80 rds. = 320 rds. 604-20=3x80rds. = 18 LEAST COMMON MULTIPLE 6 7 2 4, 6, 8, 10 13 2 2 14 2 2 15 47 77 16 3 5 2 $30 17 56 63 77 8 10 12 2 2, 3, 4, 5 456 3, 2, 5 = 120 qts. 525 = 5, 7, 3, 5 945 = 5, 7, 3, 3, 3 2 5 3 = 120 yds. 12 14 16 678 5, 7, 3 = 1051bs. 525 ^ 105 = 5 bags x $2 = $10 barley. 945 -j- 105 =9 bags x $2 = $18 wheat. 8 2 5, 6, 7, 8, 10 3 7 4=336 + 4= 340 -2=45, = 3, 3, 5 -2=75, = 3, 5, 5 3, 5 = 15 3 12 30 75 9 10 11 12 5 5, 3, 7, 4, 5 4 10 25 3, 7, 4-840cts. 425 5 2, 3, 5, 10 2 5 = $300 for each Ox 4= $1200 for all = 2, 2, 2, 7 = 3, 3, 7 = 11, 7 2 2, 3, 2 3 = 30cts.x4= 120 cts. 112 = 2, 2, 2, 2, 7 140=2, 2, 5, 7 71 i 19( 18 7 11 2 19 18 ,o each pupil >6 + 63 + 77 = 196 >-j-7 = 28 pupils 7 11 14 22 2, 2, 7 = 28 each. 3 7 9 12 11 2 22 7 3 4 =252 nuts 33456 2 2 = 154 cards -2, 3, 3 2 452 > = 3, 11 2 5 =60 in each 60 x 4= 240 marbles 3 to each 1.8 + 33 = 51, -f-3 = 17 children FRACTIONS 19 FRAC1 98 Pa 540+ 11 551 "IONS ge 74 7 49 4 _343 + 4 347 -L-^j J. w 720 + 9 729 72 T ^= 10 = ~io" 981 + 7 988 2 109$=- -9= 9 300+7 307 7 7 ?013 _280 + 13 293 14 ~ 14 *7OA i "I ^7O"I 8 240i = +_ 1 = I|l in r_ 150 + 7 157 M 12 12 1102 + 2 1104 15 15 q is 3 -240 + 3 243 uQ ~ 19 ~ 19 10 i-722 + l 723 T * 16 " 16 1R8 432 + 5 437 38 * 38 a 14 nr_H20 + 7 1127 24 ~ 24 in 1041 -520+1 521 8 8 145 _336+5_341 ** ~24 24 * jo, 169+9 178 5 5 106f = g6+_ 5 = J|L in 7 ^ 7 624+7 631 13 13 , 7 r, 136 + 5 141 4011 588 + 11 599 8 8 6 85 -1275 + 8 1283 16 ~ 16~* n o r _630 + 7 637 12 - J2 no in o 500 + 9 509 50 '"50 " 1Q7 380+7 387 10 " 10 19iV LO LO 20 FKACTIONS 101 Page 75 84 5 135 Z3 23 1 270~ 56 2 ' 378 189 21 11 = = 1818 909 101 2 8 207 3 69 23 1017 339 113 8 1011 337 12 = 1101 387 3 3 702 13 351 27 4708 2353 181 6 246 41 13 = 438 73 4 1001 3003 3 8 256 2 32 16 14 = = "20 90 45 11011 11 5 725 725 i 4350 6 711 79 15 = 981 109 6 87 3 203~ 7~ "329 7 1 6 = 841 18 7 3 129 43 750~250 "279 9 17 = 496 16 8 8 237 79 597~199 "213 3 18 5T1 9 6 555 8 111 37 975~ 195~~65 186 8 24 4 1 (19) 1T7 10 2 510 8 255 85 5 714~ 357~ 119~ 7 "33 3 2 < 20) m- IF FRACTIONS 21 *120 6 30 5 3 (21> ilT IT 9 M 90 9 9 1 4 (22) - = - = ; 180 13 2 45 5 6(23) - 6 85 17 6 (24> - 6 72 *12 3 7 (25) = 119 8 (26) - not reducible. 132 6 2 4 * 4 1 9(27) - 12 36 3 3 1 1O (28) = =- V ' 144 12 4 '99 11 14 (32) U 132 3 12 4 15 (33) - = - =- 165 15 5 *60 6 1 16 (34) - = - = 120 12 2 6 420 2 70 35 17 (35) = = 18 (36) 1 ; 15 75 5 - =- 120 8 <108 27 3 19 (37) = - = - ' 252 63 7 "39 3 20 (38) =~ 60 5 la 84 7 21 (39) - = - 132 11 5 105 3 21 7 (29) = Ia 144 3 12 4 12 (30) = = 180 15 5 5 105 T 21 3 13 (31) = =- V j 175 35 5 7 168 24 22 (40) - = - 3 539 77 *112 7 28 2 4 2 23 (41) = = = 168 42 63 287 7 24 (42) - =- 1 ' 369 9 22 FRACTIONS 65 55 1 25 (43) =- 3 81 27 26 (44) = 13 78 6 27 (45) = 18 150 3 15 5 18 (46) "99 3 3 29 5 120 3 24 8 30 (48) = = ' 165 33 11 *12 3 30 10 31 W = ^ = ^ "85 5 32 (50) - =- 102 6 '42 6 33 (51) = 34 35 34 17 28 3 4 2 10 110 11 36 (54) = 95 d 7 1 2 ( 55 > 7^=-^ 27 3 4 1 5 (57) -=- 6 180 36 4 *112 *28 7 7 < 59 ) 777= ^r == - 9(60) = "33 3 10(61) ---j 8 48 16 10 (C2) = 5 25= 5 11 (63) v ' 80 16 FRACTIONS 23 _3 75 _25 13(64) ~~ "209 19 13 (65) - = - J 220 20 3 27 9 15 60 = 17 17 1 16(67)-= T 16 li = 7 28 4 18 (69) = V J 49 "7 2 18 9 20 (70) ir M- 103 Page 76 Answers to 103 will be found in 107 104 Page 77 7 5 35 3 8 24 15 10 150 ~8~ X 5 "" 40 ' 5 8 ~ 40 ' 4 X To~~lb~ 119 13 17 289 7 1 13 13 7 ~ 1 17 ~ 17 ' 119" 17 '17 ~ 17 1 18 18 5 8 40 17 9 153 4 18 ~ 72 ' 9 8 ~ 72 ' 8 9 " 72 4 180 3 11 33 - _^_ ^ vx __ _ --- ^ . r vy _^ m *.* ' _ 27 _ 3 22 66 45 36~~4~ ss' 22 20 27 135 127 8 1016 40 24_96 ^ t c\f\ i ctr\ ' -i r- r> -I rrv ' rnr- r 04 1 rk/\ 125 _ 125 13 8 104 180 4 120~120' 24 FBACTIONS 2 3 _ 6 125 3 _375 112 _ 7 3 3 ~ 9 ' 3 3~9' 144" 9 54_18 1 _ 1 153_ 51 11 _ 561 ~~~' "~" ; ~ ' x ~~~ 41 1 25 117 1170 3 12 164 4 100 ' 10 100 ' 25 100 11 _ 77 33 _ 3 _150 48 _ 16 224 ~50~~350 ; ~77~~7 350 J ~75~~~~25~~350 25 5 15 3 1 16 5 15 80 ~ 16 ~~ 48 ' 9 ~ 3 ~ 48 ' 16 ~ 48 5 35 187 2244 209 19 1596 12 ~ 84 ' 7 ~ 84 11 ~ 1 ~ 84 401 _ 802 375 _ 125 _ 250 209 _ 19 _ 247 130~260 J 390~130~260' 220~~20~~260 7 _56 111 _ 2664 5 _ 45 1) "72"' ~3 ~72~' ~8 "7? 7 49 9 36 27 _ 9 36 ~~~~~ "~~~~ *~~~"" . 11 _ 33 17 _ 1 _ 14 29 1 __ 21 16 ~14~~ 42 ' 51 ~ 3 ~ 42 ' 58 2 ~ 42* 260 7540 501 5511 7 203 11 " 319 ' 29 " 319 ' 11 319 PBACTIONS 26 18 5 80 28 4 64 7 49 ~7~~~112 ; 49 ~~ 7 ~112' 16 112 19 130 1040 58 29 203 1 1 ~7 56 ' "l? 8 ~56' ~56~~"56~ 20 133 7 112 18 9 9 3 19 ~ 1 ~ 16 ' 32 ~ 16 J 12 4 12 U 1 10 3 15 171 342 21 2 20 ' 4 20 ' 10 20 107 Page 78 8 2 20 7 1 15 6 3 18 1 12 3 30 ' 14 2 30 ' 10 5 30 20 + 15 + 18 53 30 30 *** ;. 2 9 3 36 14 2 40 18 3 45 ~~60* 36 + 40 + 45 121 60 60 2 3 18 2 16 20 5 15 18 1 ~2f 3 24 ' 32 " 8 24 ' 36 2 12 ~ 24 16+15 + 12 43 24 24 26 FRACTIONS 5 1 8 8 1 4 613 4 ,- - - __ = > - . - _ 15 3 24 ' 48 6 24 ' 48 8 24 8 + 4+3 15 6 24 "24" 8 6 2 8 4 1 12 3 8 + 1 + 3 12 5 = = . . = . . = = = i 9 3 12 ' 48 12 ' 48 12 12 12 18 3 15 1 20 2 18+15 + 20 53 i 55 30 5 ' 30 2 ' 30 3 30 30 30 5 25 24 4 24 2 20 7 ~36 = T = 30~ ; lo = T ; ' ^ = ~3~~~30 25 + 24 + 20 69 so 30 ~ == 2-T^T 15 3 12 42 6 24 21 3 8 35 * 7 " 28~ ; 49 7 28~ J "28~~~T 12 + 24 + 21 57 28 28 ~2 2 V 12 1 8 16 1 12 28 7 21 9 - ___= - . __ = = . . ^=r, -. 36 3 24 ' 32 2 24 ' 32 8 24 8+12 + 21 41 24 " 24 ~ * 16 2 20 16 4 24 13 9 27 10 . ___ . . . . _ = _ _^ 24 3 30' 20 5 30' 20 10 30 20 + 24+27 7 1 oil 12 FRACTIONS 27 48 20 _ 1 _ 36 5 _ 1 _ 9 108' 60 3 108' 60 12 108 48 + 36 + 9 93 31 108 108 36 10 2 7 1 14 14 10+7 + 14 31 35 7 ' 35 5 ' 35 35 35 35 36 6 30 36 4 28 33 3 21 42 ~ 7 ~~ 35 ' 45 ~ 5 ~ 35 ' 55 ~ 5 ~~35" 30+28 + 21 79 35 35 33 3 9 36 2 8 5 14 1TT 9 + 8 + 6 23 12 12 16 1 2 30 1 3 45 5 15 48~ 3~"~~6~ ; ~60~~~2~~~6~' "54~ 6~ 2 + 3 + 5 10 6 6 15 _ 1 _ 20 12 _ 1 _ 12 10 _ 1 _ 15 16 "45~ 3 60 ' 60 5 60 ' 40 4 60 20 + 12 + 15 47 17 (1) 60 60 20 + 15 35 18 17 30 30' 30 30 FRACTIONS 364-40 76 45 31 T8 / o \ - 1 ' 60 60* 60 60 16+15 31 12 19 2 + 1 3 20 (4) = 8+1 9311 21 (5) = = , = v 12 12 4 ' 4 2 18+15 33 20 13 22 (6) = , = 30 30 30 30 25 + 24 49 20 29 AW f "" 2 + 3 5 5 666 20 + 12 32 15 17 32(16)^=,--^ 109 Page 78 2 3 4 5 6 7 8 1^ + 25^ + 51 = 77 T 8 T 9 10 OA FRACTIONS 12 " 14 15 IG 17 18 19 -20 21 111 Page 78 1 45ft- 2 109}! FRACTIONS 31 9 10 12 114 Page 80 2 3 4 125-13| =$111} cost 5 7 8 17 + 23 + 41=82i 237-821* = 154H Ib. 9 10 27|+34l-U + 31 T 2 6V=93H-5- 179lf$-931f = 851M mi. 12 10L& - 53 T \ =48^ ft. 13 tf-tt=A 14 37+41 + 29+54=162 T \ 9 T cd. 32 FRACTIONS 15 171^+235^ = 406111 mi . 16 235ft -171H=63Hf mi. 17 19 20 21 53H + 41]- = 95 hr. 116 Page 82 1 45H x 11 = 495W 4 1401 x 1 1 = 1540- 7 / = 1549-| 5 13^x13 = 169 + 9 = 178 FRACTIONS 33 7 49 f x 12 = 637-V = 644f 20}f x 13 = 260W 8 240 J X 13 = 3120-V- = 3124| 10^x14=130^=136^ 9 15ftxl7 = 255tt=258& 18& x 17 = 306f |= 309^ 10 104^ x 17 = 1768V = 1771| 11 78| x 17 = 1326*1*= 1340| 49H x 17 = 1133W= 12 119 Page 83 6 llx3]|=39Hmi. 7 12xl8 T V=221f hrs. 8 6xl2H=74|pp. 9 12x$728f = $8746 10 80x5* = 440 yds. 122 Page 84 (The cancellation, being simple, is not indicated) 1 25x$7f=$193f 2 19x$2|=$49f 3 160 X $65 J = $10480 4 12 x 31 J = 378 gal. 5 1 of 15 = 10 2 f of 29 = A 3 fof31 = - 6 / 4 fof23=^ 5 | of 18=12 6 f of 9 = 6 7 f of 0-0 8 of 24= 16 9 ^17=^ = 10 I of 27 = 18 UNIVERSITY \ 34 FRACTIONS 11 Iofl4= = 9} 30 |o*56=H* a 12 iofll = =7i 31 f of 19 = % 5 -= 13 f of 44 = J f^=18f- 32 f of 7=\ 5 -=3 14 a of37 = ifi=15 e 33 f of 26 = 4^= 15 f of 28 = 12 34 f of 81 = 45 16 fof!9 = V=8f 35 f of93=if*= 17 f of 7 = 3 36 f of 45=25 18 f of 14=6 37 f of 36 = 30 19 f of 24=^?-= lOf 38 fof43 = V = 20 f of 32=* 7 6 -=13f 39 fofl4 = = 21 f of 46= i f 5 -=l9f 40 f of 8=^=6 22 * of 56 = 24 41 tof49 = ^= 23 $of38=4* = 16f 42 fof53=-f- 24 fo48 = ip=18f 43 Jot 62=-4*= 25 f of 22=4^=121 44 3 of 25=M>- = 26 f of 35 = !^= 19$ 45 |ol88= V = 27 of 41 = 2-z 22$ 46 | of 18=15 28 | of 80= 4 $ fi = 44$ 47 f of 42 = 35 29 f of 72 = 40 48 |of51 = ^ = = 51f =i|^=51f = ^ = 42* FRACTIONS 36 125 Page 86 (The cancellation, being simple, is not indicated) 55 7 5 1 x = 56 11 8 13 5 1 2 X = 25 39 15 14 25 5 3 X = 15 28 6 H 7 77 4 X = 16 8 128 57 12 1 5 x = 108 19 3 75 84 1 6 x =- 105 120 2 85 81 51 7 x = 108 95 76 84 17 1 119 24 ~~ 2 55 141 235 9 X = 81 143 351 39 40 2 10 x = 60 65 5 21 13 3 11 x =- 26 14 4 19 13 247 12 x = 20 20 400 32 25 2 13 X =- 75 48 9 325 1 13 6 14 x = =1- 7 25 7 f 3 32 1 15 X = 160 9 15 7 24 3 16 X = 64 35 40 150 3 90 "I *7 - y - 151 5 151 19 7 1 T ft X 38 14 4 36 FRACTIONS 126 Page 87 (The cancellation, being simple, is not indicated) 21 15 63 9 23 207 11 -x = = 253- 248 11 29 319 2 X = 73 75 5475 x = : 8 8 64 47 60 470 4 x = =67} 677 29 7 203 60 35 1750 48 59 354 7 X== 53 100 530 8 - 42 77 1617 9 - 38 47 893 10 x== 48 23 368 12 x = =52* / o / 113 71 8023 13 x = =83*4 12 8 96 87 55 435 14 --x = -62} / t 75 101 505 15 T X T 10 11 10 100 1000 9 3 53 135 Page 90 286 13 286 5 - -^ -- = - x =n 10 5 10 13 491 7 491 2 2 T + T = T x T" 70 * d "' 41 30 12 3 30-i -- = - x - =gw 12 1 41 507 39 507 4 4 - = - X - =13 4 4 4 39 FRACTIONS 169 13 169 6 K : = x =13 dresses 6 6 6 13 1833 1833 1833 16 ; = X =4 sons 4 16 4 1833 7 3-^ = 3 x 9 = 27 divisions 33 11 33 6 8 \ = X =9 steps 2 6 2 11 116 29 116 4 16 o __ s -- = - x - = 3 4 3 29 3 10 16== -= = 12cu. ft. 136 Page 91 1797 l x x = 395 15 334 o _x-X = 223 7 3 5 4 9 35 3 x X X X = = 5$ 11998 6 11 2 7 7 4 x x = =2J 1 3 22 3 1151 5 + = ,-. =5 2 3 6 ' 6 7 66 7 7 _ 49 6 "3~~7 ~3~ X ~66~~198 40 FRACTIONS 15 15 15 16 9 -f- = X = 2 16 2 15 2 3 17 5 3 1 10 + = = , 34 12 ' 6 4 12 17 1 : =17 12 32 1235 12 -+ = 234 12 ' 25 13 - 100 1 15 -3-100=- 3 3 125 5 16 4-100=1 2 8 200 2 17 -5-100=- 3 3 50 1 18 -7-100=_ 3 6 2 8 138 Page 92 1 = | of 125 = 25; | = 6x25 = 150 2 TT= i of 144= 16; H= 11 x 16= 176 3 J = of 321 = 107; f-4xlC7=428 4 1 = 9x45 = 405 5 TI = | of 540= 108; |f =12x108= 1296 6;tiHf = 100x6=600 20 ^00=1 3 6 PRACTICAL FRACTIONS 7 T V=f of 840= 120; |f= 12x120= 1440 8 f=7x59 = 413 9 T i y= i: of 189=21; If = 13x21 = 273 10 T i T = T ^ of 910=91 ;il = llx 91 = 1001 PRACTICAL FRACTIONS 140 Page 93 41 2 175-s-875 = H$ = |- 3 of 250 = 125 ; 5 x 125 = 625 sheep 4 of $1575 = $315 ; 6 x $315 = $1890 5 i of $12300 = $6150 ; 3 x $6150 = $18450 6 T V of $18450= $1230; 7x$1230=$8610 7 8 |of-V-=! = $4* 9 i of $75 = $25 ; | = 4 x $25 = $100 value |=$100; J=$33; } =2x$33 = $66f 10 | of | = |; i = J of $5760 = $1920; 8 X $1920 =$15360 11 | of | = 1 ; i of $15360=$3840 12 5-r65==' 42 REVIEW IN FRACTIONS 13 V=i; |-i=Jleft 14 of 108=12; 20xl2=240A. 15 i- 5 2 = t = 1200. J of 1200=400. 5 x 400=2000 sheep. 16 $of = $3 17 $2325 -$1800= $525. Ans. 18 i-*=i; * of $1575 = $525. 20 i*-A=A = 8800. i of 8800=1100x13=14300 men. REVIEW IN FRACTIONS 142 Page 97 1 -*-= VxA = 6 yds. 2 Vx^ = $1176|. 3 A H-5- = 4 i ft x^V=t = $2J 4 T\xVx|xf = 3. 5 i + i = *. |-J = Ueft. J 6 20x| = $4; $44-1 = 16 Ibs. 7 $2250 x| = $3150. 8 H OJ -5-V = 1 1 xA=61 coats. REVIEW IN FRACTIONS 43 9 10 18|xl2=225 ct. sugar. 225-7-22^ = 10 Ibs. of butter. 11 | of 475 A = 190 A B's share, g of 190 A=76 A C's share, 12 22R60=Yx^ = t 13 17J + 3| + 7t + 5J=$33|. $63f -$33f = 14 15 320 x# = 1760 yds. 16 17 7H&= 18 7J-H = 19 99-T-3f = 27 cts. per Ib. f of 27cts. = 20 Jets. 20 19 x {f = V(f = 21 22 23 T V of 324=18. 18 = -^; T V=^ of 18=9. 9x19 = 171 cattle B'& 24 T 3 T of 4774 = $1302. A's share. & of $4774= $1953 B's share, $4774- (1302 +1953 = $3255) = $1519 C's share 25 2| + 2i + 1 = V 60 ^ V = 10 suits. V yds. rem. V -f- 1 = 2 44 REVIEW IN FRACTIONS 26 In one day A will do jj of the work, and B 27 6^5}=-yU-x T 2 r =$li cost per cental. 12^-5-^= = 11 centals 23 29 127xlj = $150 wheat. 18 x 11 = $22 J oats. barley. $153+$22J + $71|-=$246 total value. 30 321-r-4 = $80i per A. H T \x $801 = i-Vf-= $907f . 31 l4-47 T 2 J = lx^=^ T V 32 35xl T V=$66V carpet. 3xf = $2| curtains. 5xf = $3| chairs. $66 J + $2| + $3| = $72^. 33 22mi.xi=5^hrs., A's time. 22 mi.x T 3 T =6 hrs. B's time. B travels 1 mi. in ft hrs., in 1 hr. he travels -^ mi. in ^ hr. lmi. behind A. 34 In one day A and B do ^ of the work ; A and C, ^ ; and B and C, T V ; All will do I of the sum of iV + iV + iV= & f work in one day, or 8 days to complete work. Since B and C do T V in a day, A will do J - T V = T ^. 120-j- 7 = 17f da. A. Since A and C do ^ in a day, B will do | - ^ = ^. in 1 da., or all in 24 days, B. Since A and B do j in a day C will do j - r V= ? V in 1 day, or all in 40 days, C. 35 49|A-9A=39A. $31 90 -H39= 3190x^7 =$80. 36 $20^33 REVIEW IN FRACTIONS 45 37 ^-f-21 = i x f = f yards. 38 1G9-J-3} = 169 x T \ = 52 sheep. 39 3K- T V=V 8 xV = 4 children. 40 23f-r- 1 ^ = ^x- 1 /=$76. 41 62J-v-50 = if^x 7 V=$f Per sack. 12x| = $15. 42 H T V=H spent. f-^=ff saved. 106 = ff. fS=106x M=$140. 43 ! ofB's + of B's = ! of B's=,$1728. 1 728 -^-f- = $1296 B's money. of $1296 =$432 A's money. 44 2x5x4 45 81J-7-= 1 -xf 46 588-7- 24J = 24 cattle. $27f -$24=$3}- gain on each. $3} X 24= $78 total gain. 47 48 Let | = C's share; then A's=f of C's, and B's twice f , or | of C's. | + f + f , or f of C's share = $2835. ^ = I of $2835 = $315. = 2x$315 = $630 A's share, f = 4 x $315 = $1260 B's share. | = 3x$315 = $945 C's share. 49 if of - J f 4 = 40 Ibs. $34-^-40 = $.85 per Ib. 46 REVIEW IN FRACTIONS 50 Let A's=f, then B's=f of A's, and C's 1 of f = |of A's. I + 1+1, or V of A's = $15303. = & of $15300 =$1020. 3 x $1020 =$3060 A's money; 5 x $1020 = $5100 B's money; 7x$1020=$7140 C's money. 51 5J-H = $ cost of one cord. 17 J x V = JJ tf Li = $144 1 total cost. 52 35ff + 47fH17ff=100||A, 100fx 40 = $4036 Ain't ree*d 53 1000-r IJ = 1000xf=800 centals. 54 + =l Sum. - = Diff. 3x- = I Product. 55 5Jx40 = 220 cts. for butter; 10 Jx 18 = 186 cts. for eggs; 220 cts. + 186 cts. = 406 cts for both . 406cts. -r- 7 J = 406 X 2 4 5 = 56 Ibs. 56 $41 T %-$3f = $37}. $37J-M2J=VxA = $3. 57 Six $15= 127* cost of coal. 9| x 7^ = $72 1 cost of wood. $127 H $72 = $200 total cost. 58 40 x $63 =$2520 cost. ^ of 40 A. x $72 = $900. ,&of40A.x $59 = $357. 21^ Ax $65 = $1408 J. $900 +$357 + $1403 J = $2665J total receipts. $2665J - $2520= $145} gain. 59 f of 189 = 81. 81 -r-567 = } Ans. Let 1 = A's loan, then will 2= B's, and 3 the total loan. A paid back of 1 = J. B paid J of 2 = 1. Total pay- ments= 1 J, or of the whole. $150 = \, total loan = $300, of which A had J, or $100, and B , or $200. REVIEW IN FRACTIONS 47 61 35 x 47= V- X 4*= ^i^= 1692 yds. 62 63 64 3651x24 =8766 hours. 65 14 x $23| = $329 cost of cows. 11 x $85f = $9431 cost of horses. 50x$2i- = $137costof sheep, $329 + $9431 + $137*= $14^1- total cost. $1500 - $14091= $901 left. 66 T V of 15 = $1* gain. $12| cost + $! gain =$141 S. P. 67 9f f = -V^. W + 1 & = Vo 3 ; 533 mi. = 5 5 3 o 3 o f distance to San Jos< 533^. 5^=50 mi. to San Jos6. 533 mi. - 50 mi. = 483 mi. to Los Angeles. 68 For every day the first worked, the second worked three days, and the third two days, 1 + 3 + 2=6 parts to the work. $12.30+6= $2.05 one part, or share of first; 3 x $2.05 = $6.15 share of second; 2 x $2.05 = $4. 10 share of third. 69 3 + 3 l = 6 mi. apart in one hour. 6?xl3|=93|| mi. total distance. ' 70 3} - 3f = & mi. in 1 hr. i of 13= 1J mi. total distance. 71 24831-r225|= - 9 - 9 ^ x ^= 11 bbl. 72 2B-f=fxf=6 collars. 73 81^ + 98|t+105|f + 112M=$398f total value. 398f+4= $99^ average value. 74 35x$15=$342C. + $17iG. = $560S. P. 560+35 = $16 each. 75 T 4 T of 375= 100 oranges. tV o* 375 = 75 oranges. 375 - 175 = 200,xl|cts. = 350cts. 48 REVIEW IN FRACTIONS 76 30J + 42$=72&yds. 241K72 2 9 y=$3J per yard 77 | - + 1 = | of dist. W. traveled. $ = $of 5f=f mi. 4xf = 2f mi. dist. R. traveled. 5x1 = 3 mi. dint. W. traveled. 78 365 - 60 = 305 days. 305 x f = $228|. 79 28|-Ml| = J-pX2 2 = $f per box. 22}-H = -Vx$ = 9 boxes. 80 2|x| = f|. |f + ff = ff of Frank's. 11 = 24^; T V = $J. 33 x$J = $16^ Fred's share. 16 x$= $8 Frank's share. DECIMAL FRACTIONS 154 Page 108 75.14000 3 7.070700 .12500 20.000300 131.13100 171.411200 .07850 27141.750000 7.00700 480.700000 .13147 626.114000 1389.90000 .070107 .00910 .141000 1603.52207 28347.257307 857.14000 4 82.10730 85.07140 1.01010 .07408 3150.07100 .00291 4090.07000 405.01000 293.02930 78.78000 47.14100 2.04040 29.64100 7814.00200 10.10000 9242.12079 7703.1697 DECIMAL FRACTIONS 49 10 75.140 131.131 7.007 1389.9 1603.178 .125 .0785 .13147 .0091 "34407 857.14 20404 480.7 3150.071_ 4489.9514 85.0714 7814.002 526.114 4090.07 12515^2574 .07408 7.0707 .070107 293.0293 300.244187 .00291 20.0003 .1410 47.141 11 12 13 14 15 16 405.01 171.4112 82.1073 29.641 688.1695 78.78 27141.75 ]. 01010 10.1 27231.6401 25.25 9.114 7.5 11.008 52.872 74.0099 11.00045 .004 .04 85.05435 .75 .0075 40.40 4000.004 4041.1615 .91 9.1 .4 1.21 11.62 9. .057 5.011 72.6 86.668 50 18 19 20 87.54 90.8 117.041 _?5_i?09 320.39 238.012 171.125 328.01 190.008 927.155 .2 2.4 12. 17.5 32.1 DECIMAL FRACTIONS 21 22 2.496 7.125 .0125 .025 9.6585 75.14 .125 75.015 857.14 85.0714 772.0686 857.14 .07408 857.00592 857.14 .00291 857.13709 857.14 405.01 452.13 155 Page 108 6 10 20.0003 7.0707 12.9296 171.4112 7.0707 164.3405 27141.75 7.0707 27134.6793 82.1073 1.0101 "81.0972 DECIMAL FRACTIONS 5] 158 P 75.14 75.14 30056 7514 37570 52598 age 109 6 .13147 75.14 52588 13147 65735 92929 5646.0196 .125 75.14 500 125 625 875 9.39250 131.131 75.14 9.8786558 7 1389.9 75.14 55596 13899 69495 97293 104437.086 8 .0091 75.14 524524 131131 655655 917917 364 91 455 637 9853.18334 .0785 75.14 3140 785 3925 549') 5.898490 7.007 75.14 .683774 9 75.14 1.25 37570 90168 9.39250 10 .125 .125 625 1500 28028 7007 . 35035 49049 526.50598 .015625 62 DECIMAL FRACTIONS 11 12 13 14 15 16 17 131.131 .125 655655 1573572 16.391375 .0785 .125 3925 9420 18 85.0714 131.131 = 67.28549 6.67810490 .005815280 .000228435 31.793285 11155.4977534 19 .07408 131.131 9.71418448 20 .00291 131.131 .0098125 7.007 .125 35035 84084 .875875 .13147 .125 .38159121 21 405.01 131.131 53109.36631 22 78.78 131.131 10330.50018 23 2.0404 131.131 65735 157764 .01643375 1389.9 .125 267.5596924 24 7814.002 131.131 69495 166788 173.7375 .0091 .125 1024657.896262 25 857. 14 x. 0785 26 85.0714 x" = 27 .07408 x " = 28 .00291 x " = 29 405.01 x " = 455 1092 .0011375 857.14 131.131 112397.62534 DECIMAL FRACTIONS 53 30 78.78, x .0785 = 6.184230 31 2.1404 x .0785 = .1601714 32 7814.002 x. 0785 = 613,3991570 33 7.0707x7.007 = 49.5443949 34 20.0003x7.007= 140.1421021 35 171.4112x7.007 = 1201.0782784 36 27141.75x7.007= 190382.24225 37 480.7x7.007 = 3368.2649 38 526.114x7.007= 3686.480798 39 .070107x7.007= .491239749 40 1410 x 7.007 = .9879870 41 7. 0707 x. 13147 = .929584929 42 20.0003 X. 13147= 2.629439441 43 171.4112 x. 13147= 22.535430464 44 27141.75 x. 13147 = 3568.3258725 45 .13147x480.7 = 63.197629 46 526.1 14 x. 13147 = 69.16820758 47 .070107 X. 13147 = .00921696729 48 .1410 X. 13147 = .018537270 54 DECIMAL FRACTIONS 49 82.1073x1389.9= 114120.93627 50 101010x1389.9= 1403.93799 51 3150.071x1389.9= 4378283.6820 52 4090.07 x 1389.9 = 5684788.293 53 293.0293x1389.9= 407281.42407 54 47.141x1389.9 = 65521.2759 55 29.641x1389.9 = 41198.0259 56 10.1x1389.9 = 14037.99 57 82.1073 X. 0091 = .74717643 58 1. 01010 x. 0091 = .009191910 59 3150. 071 x. 0091 = 28.6656461 60 4090.07 x. 0091 = 37.219637 61 293.0293x.0091= 2.66656663 62 47. 141 x. 0091 63 29.641 X. 0691 64 10.1 x. 0091 = .4289831 .2697331 .09191. DECIMAL FRACTIONS 55 160 Page 109 1 7 25 x. 06 =43.5 2 42.5 x. 8 = 34 3 7.84 x. 125=. 98 4 17.28 X. 03 = .5184 5 4.096 X.12=. 512 6 256 X.16= 42.66f 7 2.444x1 = .611 8 515.1x^ = 171.7 9 480x^=24 10 .764x.l75 = .1337 12 1. 044 x. 9 = 9. 396 13 72400 x T V = 4525 14 245.4 x. 15 = 36.81 15 3.55 x. 8= 2.84 16 96X T V = 2 ^ 8 17 250 x. 28 = 70 18 1400x1.05 = 1470 19 380x1.2=456 20 920 X. 45 =414 162 Omitted PRACTICAL WORK IN DECIMALS 168 Page 113 1 240.25x.63=151.3575 bales. 2 475 Ibs. x .63 = 299.25 Ibs. 3 17.6+23.25+42.625 = 83.475 A. 83.475 X $40 =$3,339. 56 PRACTICAL WORK IN DECIMALS 4 .2 of '3125 = .0625 sold. .3125 - .0625 = .25 left 5 36 X $.12| = $4.50 6 648.96-5-8 = 81.12 A. 7 27-J-2.25 = 12 books 8 6.75 mi. x 11 = 74.25 mi. 9 2150.42 x 5.16f= 11110.50 cu. in. 10 $1.37 Jx 296= $407 11 272.25 ft. -f- 16.5 f t. = 16.5 rd. 12 Their sum, or 187.46 mi. 13 187.46 mi.-r-6 = 31.24j mi. 14 278.15 + 392.14 + 171.9 + 429.51 + 530.875 = 1802.575A. 3218A. - 1802.575A. = 1415.42JA. 15 42-^2.625 = 16 pairs 16 231 cu. in. x 31 .5= 7276.5 cu. in 17 (32.0625 + 28.4375) x 2= 121 rds. around 18 5280 ft. -7-21.96 ft. = 240.43 turns 19 12 x $81. 875 = $982.50 cost. $1000- $982.50=$17.50 left 20 $.162.75-^ $7.75 = 21 cords PRACTICAL WORK IN DECIMALS 21 7.231 A. + 9.124 A. + 6.715 A. = 23.07 A. -=-3 = 7.69 A. 23.07 A. + 7.69 A. = 30.76 A. 22 30.76 x $50 =$1538. 23 .08 +.16 + .5 = .74 spent; 1.00- .74-+. 26 left. .26 =$26, the whole = $26 +-.26 =$100. 24 .33 +.45=. 78 . 1.00- .78 = .21. 25 15.87J + 1 26 63x$7f = 27 4fx8=38mi. 38 +-.59375 = 64 times. 28 (15^+10.1875) x 2=51 rds. around. 51x3 = 153 rds. of rail; 153xl6i = 2524} f t . 2524.5-f- 7.5 = 336.6 rails. 29 Their sum= 112.241 in. ^-5= 22.4482 in. average 30 " 2.125 gal.x60 = 127i gal. 31 17.125 = $9.60=$164.40. 32 4.64 mi. + 5.16 mi. = 9.8 mi. distance apart in one hour. 9.8 mi. x 13 = 127.4 mi. total distance apart. 33 107.8 mi.-j-9.8 mi. = 11 hrs. 34 48 X 3.1416= 150.7968 sec. 35 8000 x 3.1416=25132.8 mi. 00 BILLS 172 Page 121 1 To 5 yds. Ribbon . @ .12' 621 " 11" Bl'kCasm're " 1.60 17 60 " 4doz. Buttons . " .30 1 20 " 2yds. Silesia . " .20 40 " 10 yds.Sheeting " .18 1 80 " 1 pr. Gaiters, 3 50 25 14 2 To 5 gals. Kerosene Oil @ .25 1 25 " 3 prs. Blankets . " 6.50 19 50 " 25 Ibs. Brown Sugar " .07 1 75 " 3doz. Eggs . . " .20 60 " 1 Turkey, 12 Ibs. " .22 i 2 64 " 50 Ibs. Potatoes . . " .01J 75 26 49 3 1880 Mar. 3 To 2 Ibs. Steak . @ .12J 25 it 4 " 41 Ibs. Roast Beef" .12 54 (t 5 " 1| Ibs. Sirloin " .15 26i it 6 " 51 Ibs. Mutton " .10 55 8' " 1 A&CHam,151bs" .19 2 85 " ] " 3 Ibs. Veal Roast " .14 42 4 87* 4 PETALUMA, JULY 17, 1888. MR. M. S. JOHNSON, To JOHN SMITH, Dr. To Services, 12 da. @ $1.50 18 00 To Idoz. Wooden Chairs @ $1. 6 00 1 Lounge, 12 50 1 Bed Room Set, 22 75 3 Fancy Chairs @ $2.25 1 Extension Table, 6 7 75 50 1 Center Table, 4 00 59 50 MR. GEO. SIMS, BILLS 59 SAN FRANCISCO, JULY 19, 1888 To S. WILSON, Dr. To 10 tons Hay, @ $10.00 100 00 To 8 doz. Oranges, @ .15 " lOlbs. Nuts, " .10 " 8 Lemons, " .02 ' ' 5 Ibs. Mixed Candy ' ' .20 " 1 box Apples, " 7 boxes Bt'wb'r's, " .45 1 1 1 1 3 20 OJ 20 00 00 15 7 55 To 12 Pencils, @ .05 60 " i ream Note Paper, 40 "4 Note Books, @ .10 40 ' 1 Rubber Eraser, 05 " 1 pkg. Envelopes, " 2 Fifth Readers, @ .85 1 10 70 " 2 School Geog., @ 1 .40 2 80 6 05 To 14 yds. Print, @ ,12 1 68 " 3 Ibs. Butter, " .28 84 " 4 bars Soap, " .10 " 1 pr. Child's Shoes, 1 40 75 " 25 Ibs. Flour, @ .02-J 62^ " 1 can Lard, 65 " 2 Ibs. Cheese, " .17 34 6 281 60 WEIGHTS AND MEASUKJfiS PART II WEIGHTS AND MEASURES Linear Measure 174 page 123 30 3 mix 320 + 2 rds. = 962 rds.,x5 + 4| yds., = 5295. 66 yds., x 36 = 15.887 ft 31 3 yds. x 36 + 2 in. = 110 in. 110 in.^36=3.05f yds. 32 1 mi. x 320 + 2 rds. = 322 rods., X 16J + 2 ft. = 5315 ft. 5315 ft. -:-5280=1.0066 mi. 33 3rds. x5 + 4yds. = 20} yds., x3 + 2 ft. = 63J ft., x 12 + 2 in. = 768 in. 768 in -J- 12 =64 ft. 34 2rds.x5 + l yd. = 12 yds.,x3 + 2 ft. = 38 ft.,x!2 + 6 in.= 462 in. 462 in. -M2= 38.5 ft. 35 1 mi. 1 ft. = 5317ft.,x!2 + 6in. = 63,810in. 63,810 in^36= 1772.5 yds. 36 3mi.x320 + 80rds. = 1040rds.,xl6}=17,160ft. 17,160 ft. -7-5280 =3. 25 mi. 37 2 mi. x 320 + 2 rds. = 642 rds., x 16}+ 3 ft. = 10,596 ft. 10,596 ft. -5-5280 = 2.0068+ mi. 38 693 in. 693in.^l98=3.5 rds. WEIGHTS AND MEASURES 61 39 4 mi. x 320% 240 rds. = 1520 rds. , x 5 } = 8360 yds. 8360 yds. ~- 1760 = 4. 75 mi. 40 3 mi. x 320 + 8 rds. = 968 rds., x5J + 3 yds. = 5327 yds.,x3 + 2} ft. = 159831 ft. 15983} ft,-r 3=5327.75 yds. 41 7rds. = 1485 in. 43 4 f rds. -f- 320 = ? f ? mi. 44 f mi. = .83Jmi. 45 . 375 mi. x 320 = 120 rds. 46 2ft. xl2 + 6fin. = 30| in., -7-198=. 1553+ rds i 47 65 rds. x 51 + 2 yds. = 359^ yds., x 3+ 2 ft. = 1080 ft.,x!2 + 6 in. = 12,972 in. ,-r63,360= .2047 + mi. 48 25 rds. x5| + 41 yds. = 142 yds., X 3= 426 ft. 35rds.x5 + yds.,x3 + 2| ft. = 589J ft. 49 42 rds.x5i + 2 yds. = 233 yds.,x36 + 4.3 in. = 8342.3 in.,-f 63,360=. 1324 + mi. 50 6 ft. x 12 + 8.5 in. = 80.5., -r 198=. 4065+ rdB. 51 3^ yds. x 36= 126 in. 7 yds. x 36 + 4 in. = 256 in. 52 165 rds. x5i + 2 yds. =909| yds., x 3 + 2 ft. = 2730! ft., x 12 + 9 in. .32,775 in., 4- 63,360 =f iff mi. 53 2 yds. x 3 + 2 ft. = 8 ft., x 12 + 2 in. = 98 in. 3yds.x36 = 108 in. 98^-108=|f 62 SURFACE MEASURE 54 = 19,684 in.,4-63,360= T V8\V mi. 177 Page 128 9 39.37 in. X 5.24= 206.2988 in., 4-12 = 17ft. 2.2988 in.; or 5 yds. 2ft. 2.2988 in. 10 39.37 in. x 35.428 = 1394.80036 in.,-M2=116 ft. 2.80036 in. 116 ft. 4- 3 = 38 yds. 2 ft. Ans. = 33 yds. 2 ft. 2.80036 in. 11 39.37 in. x 5785 = 227,755 .45 in., 4-63,360 = 3.594+ mi. 12 7,856,918 in.4-39.37= 199,566.11 + meters. SURFACE MEASURE 178 Page 129 18 1 sq. rd. x 30} X 9 = 272 sq. ft. , x 144 = 39,204 sq. in. 1 A. x 160x30} = 4840 sq. yds., x 9 =43,560 sq. ft. 19 2 A. x 160 + 40 sq. rds. = 360 sq. rds., x 30} = 10,890 sq. yds., X 9 + 17 sq. ft. = 98,027 sq. ft. .20 3 A. x 43,560 =130,680 sq. ft. 21 3 sq. mi. x 640=1920 A., x 160+17 sq. rds. =307217 sq. rds., x30} + 4 sq. yds. = 9,293,318} sq. yds. 22 3476 sq. in. 4- 144 = 24& sq. ft. 23 98756 sq. in. 4- 144 =685 sq. ft. 116 sq.in. 24 7856 sq. ft. 4-9 = 872 sq. yds. 8 sq. ft. 872 sq. yds.4-30 = 28 sq. rds. 25 sq. yds. Ans. = 28 sq. rds., 25 sq. yds. 8 sq ft. SURFACE MEASURE 63 25 48413 sq. yds. -j- 30^ = 1600 sq. rds., 13 sq. yds. 1600 sq. rds.' 4-160 = 10 A. Ans. = 10 A. 13 sq. yds. 26 189.5 rds. x 150 rds. = 28425 sq. rds. = 177|i A. 177fl A. x $75f =$13,457.46 + . 27 37 A. x 160 +128 sq. rds. = 6048 q. rds. 170 A.xl60 + 16 sq. rds. = 27 .216 sq. rds. 27,216 sq. rds. - 6048 sq. rds.= 21,168 sq. rds. 21,168-;- 27,216= . 179 Page 130 10 1 sq. mi. x 640 x 10 = 6400 sq. ch., x 16=102,400 sq. rds., x 625 = 64,000,000 sq. 1. 11 160 A. = ! sq. mi. 64,000,000 sq. 1.^4 = 16,000,000. 12 2 sq. rni. x 640 + 6A. = 1286 A., x 10+9 sq. ch. = 12,869 sq. ch. 13 1 A.xl0xl6x625 = 100,000sq. 1. 14 1 sq. mi. x 640 + 1 A. = 641 A., x 10+1 sq. ch. = 6411 sq. ch., X16 + 1 sq. rd. = 102,577 sq. rd. 10,2577 sq. rd.x625 = 64,110,625 sq. 1. 15 842,590 sq. 1.4-625 = 1348 sq. rd. 90 sq. 1. 1348 sq. rd.-f-16=_ 84 sq. ch. 4 sq. rd. 84 sq. ch.-rlO = 8A., 4 sq/ch. Ans. 8 A. 4 sq. ch. 4 sq. rd. 90 sq. 1. 16 25,373,896 sq. l.-r 625 = 40,598 sq. rd. 146 sq. 1. 40,598 sq. rd. -=-16=2537 sq. ch. 6sq. rd. 2537 sq. ch. 4- 10 = 253 A. 7 sq. ch. Ans. 253 A. 7 sq. ch. 6 sq. rd. 146 sq. 1. 17 98,754sq. rd.^!6=6172sq. ch. 2 sq. rd. 6172 sq. ch.-f-lO = 617 A. 2 sq. ch. Ans. 617 A. 2 sq. ch. 2 sq. rd. 64 CARPETING AND PLASTERING 18 9867 sq. ch.^lO=985 A. 7 sq. ch. 985 A.4-640= 1 sq. mi. 345 A. Ans. 1 sq. mi. 345 A. 7 sq. ch. 19 75,328 sq. rds.-r 16=4708 sq. ch., -=-10=470 A. 8 sq. ch. 20 46 ch. x 37 ch. = 1702 sq. ch. 42 A . 5 sq. ch. = 425 sq. ch. 1702-425=1277| sq. ch. 1277^1702 = 1 21 5 ch. x 100 = 500 l.,x 25 = 12,500 sq. 1., -r 100,000 = I A. lost. 12 A. - | A. = 11|A. lH-rl2 = ff cultivated. 22 S. 5 ch. + S. 3 ch= S. 8 ch. .'. Must measure north the same distance. 1st rectangle = 10.6 ch. x 5 ch. = 53 sq. ch. 2nd rectangle =5. 3 ch.x 3 ch. = 15.9 sq. ch. 53 sq. ch. + 15.9 sq. ch. = 68.9 sq. ch., -r 10 = 6.89 A. 180 page 132 3 234.56m.xl84.25m.,=43,217.68sq. m.,-MOO=432.1768ares 4 6 m. sq. = 36 sq. m. 36 sq. m. -6 sq. m. = 30 sq. m. 5 160 A. -t- 2 .47 = 64.777327 ha., x 100 =6477.7327 ares. CARPETING AND PLASTERING 181 page 132 1 I5f ft.-H yd. = 7 breadths. 17 ft.-=-3=5f yds. 5 yds. x7 = 39| yds. 2 = 46|yds. crosswise. 17 ft.-j-3=5f yds., or 6 breadths., x 7 yds. = 46f yds. lengthwise. 3 11 ft. = 3f yds. ; 15 ft. =5 yds. 5-r| = 6, of 7 breadths, x 3f = 25 yds. crosswise. 3-r2 = 5 breadths, x 5 = 25 yds. lengthwise. CARPETING AND PLASTERING 65 4 24 ft. -7-3 = 8 breadths. | of 8 = 1 yd. for matching. 19 ft. -f- 3=6jyds.,x8+lyd.=51f yds., x $1.25 = $64.58 J. 5 13^ ft. -7- 1 yds. = 6 breadths. J x 6 = 1 yds. for matching. 18 ft. 4-3=6 yds. 6 yds.x6 + H yds. = 37i yds., x $2.75 = $103.12^. 6 (18 ft. + 20 ft.) x 10 ft. x 2= 760 sq. ft., sides. 18 ft. x 20 ft. = 360 sq. ft., ceiling. 1120 sq. ft., sides and ceiling. 6 ft. x 2 ft. x 2= 18 sq. ft. , windows. 7 ft. x 3 ft. = 21sq. ft., door. 57 sq. ft. -5-2= 28.5 sq. ft., allowance. 1120 eq. ft. -28.5 sq. ft. = 1091.5 sq. ft. -r 9 =121. 277 sq. yds., x$.27 = $32.74J. 7 (11 ft. + 12 ft.) x 12 ft. x 2 = 552 sq. ft., sides. 11 ft. x 12 ft. = 132 sq. ft., ceiling. 684 sq. ft., sides and ceiling. 6 ft. x 2 } ft. = 15 sq. ft. , window. 7 ft. x 2$ ft. = 18 sq. ft., door. 33f sq. ft.-7-2=16f sq. ft. 684 sq. ft. (s. and c.) - 16$ sq. ft. (allowance) = 667 sq. ft. 667| sq. ft. x 17 = ll,341f sq. ft.-r9 = 1260H sq. yds. 8 (90 ft. + 65 ft.) x 24 ft. x 2= 7440 sq. ft., sides. 90 ft. x 65 ft. = 5850 sq. ft., ceiling. 1^290 sq. ft. 10 ft. x 3 ft. x 13 = 390 sq. ft., windows. 9 ft. x 4 ft. x 4= 144 sq. ft., doors. 534 ft. -7-2 = 267 sq. ft. 13.290 sq. ft, - 267 sq. ft. = 13,023 sq. ft., + 9 = 1447 sq. yds. 66 CARPETING AND PLASTERING 9 (16 ft. + 24 ft.) x 9 ft. x 2 = 593 sq. ft., sides. 16 ft. x 24 ft. = 384 sq. ft., ceiling. 1104 sq. ft., -f-9 - 12 = 110 sq. yds. 10 (24 ft. + 15J- ft.) x 10 ft. x 2 = 795 sq. ft. , sides. 24 ft. x 15 J ft. = 373f sq. ft. , ceiling 1168| sq. ft.-f-9-14 sq. yds.= 115H sq- yds., x $.30 = $34.75 11 (18ft. + 15ft.)xlOft.x2=660sq. ft.,-r-9 = 73 sq. yds. -20 sq. yds. = 53| sq. yds. 53 J -5- (8x3) = 10 rolls, -f- $.95 = $9.50 12 (17 J f t. + 24f ft.) x 10 ft. x 2 = 843 sq. ft. , sides. 17 J ft. X 24 ft. = 431f sq. ft. , ceiling. 1275 sq. ft. -7-9 - 50 sq. yds. = 91$ sq. yds. x $.33 =$30.25 13 843 sq. ft., sides^9 = 93^ sq. yds. -50 sq. yds. = 43^ sq. yds. 8x|f=4sq. yds. in a roll. 43U-r- 4=1 05f rolls, x $.75 = $8.19. 14 30 ft. x 25 ft. x 2 = 1500 sq. ft., x 144= 216,000 sq. in. 216,000 sq.in. -f- (5 in. x 4in.) = 108,000 sh'gles-r- 1000= 10.8 M. 15 100 ft. x 4 ft. -f- (8 in. x 4 in. -7- 144) = 1806 bricks. 16 16 in. x 24 in. x 8404-144=2240 sq. ft. .17 (18 ft. + 16 ft.) x 12 ft. x 2=816 sq. ft., sides. 18 ft. x 16 ft. = 288 sq. ft. , ceiling. 1104 sq. ft., sides and ceiling 8 ft. x 2| ft. x 2 -=-2 = 32 sq. ft., windows. .8 ft. x 3 ft. x 2-h2 = 24 sq. ft. , doors. 56 sq. ft. allowance 1104 sq. ft.-56 sq. ft. = 1048 sq. ft.,-j-9=llfi$ sq. yds., X .$.37=$43.66. SOLID MEASURE 6/ 18 3 ft. x T 8 * ft. x 2 = 4 sq.ft. both sides ; 4 ft. x & ft. = 2f sq.ft.top. 4 sq ft. + 2 j sq. ft. = 6| sq. ft. x 144-i- (4x4) = 60 tiles. SOLID MEASURE 183 Page 135 2940cu. ft.,-5-27 = 108f cu. yds. 2 18 x 1 2 x 9} ; = 1889 cu. ft., +1 28= 15ff cords. 12 9x4-f-144x24 = 6cu. ft. 16 13 c. yds. x 27 +11 cu. f t.= 332 cu. ft., x 1728 = 625,536 cu. in. 17 9 cu. yds. x 27 + 4 cu. ft. = 247cu. ft., x 1728 + 13 cu. in.= 426,829 cu. in. 18 159,728 cu. in. 1728 = 92 cu. ft. 752 cu. in. 92 cu. ft. 27 = 3cu. yds. 11 cu. ft. Ans. 3cu. yds. 11 cu. ft. 11 cu. ft. 752cu.in. 19 9 cu. ft. x 1728 + 828 cu. in. = 1638 cu. in. 7 cu. ft. x 1728 + 932 cu. in. = 13,028 cu. in. 16,380 cu. in. + 13.028 cu. in. =: 29,408 cu. in. 20 12x11x9 = 1188 cu. ft.,^27 = 44cu. yds. 21 30 in. X24in.x2in. = 1440cu. in. 22 27 x 175 Ibs. = 4725 Ibs. 23 7ft.x9ft.x7ft. = 441cu. ft., x 1728 = 762,048 cu. in. 24 128 cu. ft. x 11 = 192 cu. ft.,+-(3| ft. xo ft.) = 10ff ft. 25 7 ft. x7 ft. x7 ft. = 343 cu. ft., -5-27= 12 cu. yds. 19 cu. ft. 68 SOLID MEASUKE 26 ft. x 4J ft. x 6 ft. = 1512 cu. ft., -h 128 cu. ft. = 11|| cords. 27 16ft.x4ift.x7ft. = 520cu.ft.,-M28cu. ft. = 4^ cords., x $6.50=$26.41. 28 247 cu. ft.^27 = 9f} cu. yds. 29 63 ft. x 157 ft. x 8 ft. = 79,128 cu. ft.,-^27 = 2930 cu. yds. 30 (150 ft. x 60 ft. -r- 2) x 9 ft. = 40,500 cu. ft.,-5-128 cu. ft. = 316$$ cords, x $9.60= $3005.86. 31 20 cu. ft. X1728 + 432 cu. in. = 34,992 cu. in.,-r-46,656 cu. in. = 75 cu. yds. 32 216 cu. in.^!728=.125 cu. ft. 33 648 cu. in. ^46,656 = T V cu. yd. 34 .75 cu. yd. x 46,656 = 34,992 cu. in. 35 .975 cu. yd. x 46,656= 45,489.6 cu. in., -S- 1728 =26 cu. ft. 561.6 cu. in. 36 .375 cas. x 128-48 cu. ft. 184 Page 137 3 28.5 steres. x .276= 7.866 cds. 4 7.2 in. x 1.7 m. x 2 m. = 24.48 cu. m. or steres. 24.48 steres x. 276 = 6. 75648 cds. STONE AND LUMBER 69 STONE AND LUMBER 185 Page 138 1 (22 ft. + 45 ft.)x8 ft. x H ft. x 2 = 1608 en. ft.4-16 =97^ perch, x $5.25 = $511. 64. 2 (30 ft. + 45 ft.) x 20 ft. x 1 ft. x 2 = 3000 cu. ft. 7 ft. x 2 J ft. x lft.xlO=175cu. ft.;. 3ft.x8ft.xlft.x4=96cu. ft.; 175 cu. ft. + 96cu. ft. = 271cu. ft. 3000 cu. ft.-271cu. ft = 2729 cu. ft., x 21 = 57 ,309 bricks. 3 (58 ft. x 25 ft.) x 44 ft. = 7304 sq. ft. 8 ft. x 3 ft. x 29 = 696 sq. ft. 7304 sq.ft. -696 sq. ft., = 6608 sq. ft., xl ft. = 9912cu. ft. x21 = 208,152 bricks-r- 1000 = 208.157 M.,x $4 =$832.61. 4 (9 rds. + 7 rds.) x 2 x 16* x 5 ft. x 1 J ft. = 3960 cu. ft. = 3960 cu. ft.^-16j = 240 perches. 5 40 rds x 4 = 160 rds. x 16 } x 4 ft. x 2 ft. -f- 16 J = 1280 perches. (46 ft. + 34 ft.) x 2 = 160 ft. x 20 ft. = 3200 sq. ft. 8 ft. X 3 ft. x 12 = 288 sq.ft.; 7f ft.xSJft. x6 = 149 sq. ft. ; 288 sq. ft.-F 149 J sq. ft. = 437 J Rq. ft. 3200 sq. ft! - 437 sq. ft. = 2762J sq. ft. (surface) xl ft. = 4143|cu. ft. X 21 = 87,018| bricks. 8 lof 16 + 11 = 131, average width. 13*xl5-Hl2 = 16ft. 9 30x8x8-i-12 = 162ft. 10 40xl4xll-MOOO=.513jM.x$32.50 = $16.684. 11 9^12x14x3-7-12=378 ft. -7- 1000 = .378 M.,x$40 = $15.12 70 LIQUID MEASURE 12 45x18x2x4^12 = 540 ft. 13 328x12x84-12 = 2624 ft., -5- 1000= 2.624 M.,x$24=$62.98 14 12x8xl-i-12 = 8 ft. 15 24x10x1 = 240 ft. 16 8 x 14x10x34-12= 280 ft. 17 50x12x1 = 600 ft. 18 10x18x4x6-5-12 = 360 ft. 19 8 x 18x16x24- 12= 384 ft. 20 11 x (18 + 11) 4-2x1 = 13^ ft. 21 2 x 19 X 15 x 154- 12 = 712 J ft. LIQUID MEASURE 186 page 140 13 Ibbl.x31jx4 + 2qts. = 128qts.,x2 + l pt. = 257pts. 14 5bbls.x311x4 + 6qts. = 636qts. 15 1-bbl. x 31^x4= 126 qts., x 2 = 252 pts. 16 5 bbls. x 311 x 4+ 2 qts. = 632 qts,. x 2 + 1 pt. = 1265 pts. 17 2 gals, x 4+1 qt. = 9qts.,x2xl pt. = 19pts. 18 1 bbl.x3Ux4 + 3qts. = 66 qts. ^ LIQUID MEASURE 71 19 1 bbl.xSlJxJ gal., = 31| gals., x 4+1 qt. = 127 qts.,x2 = 1 pt. = 255pts. 20 7856 qts4-4=1964 gals., 4-31^=62 bbls. 11 gals 21 9563 pts. 4- 2 = 4781 qts. 1 pt. 4781 qts. 4-4=1195 gals. 1 qt. 1195 gals.4-3H = 37 bbls. 39 gals. Ans. 37 bbls. 39 gals. 3 qts. 1 pt. 22 9543 qts.4-4=2385 gals. 3 qts. 2385 22 gals. 2 qts. 75 bbls. 22 gals. 2 qts. + 3 qts. = 75 bbls. 23 gals. 1 qt. 23 86543 pts. 4-2 = 43271 qts. 1 pt. 43271 qts. 4- 4 =1041 7 gals. 3 qts. 10417 gals.4-31i=343bbls. 12 gals. 2qts., + 3 qts. Ipt. = 343 bbls. 13 gals. 1 qt. 1 pt. 24 6754 gals. 4- 31 = 214 bbls. 13 gals. 25 16 gals, x 4x2 = 128pts. 26 2 bbls.x31 + 4 gals. = 67 gals.,x4-f-2 qts. = 270 qts., x 2 + 1 pt. = 541 pts. , x $.05 = $27.05 27 41 gals. 3 qts. 1J pts. 25 " 7 " 1 " 9 (( 3 " Ifr " 78| gals, x $.75 = $59.06 78 gals. 3 qts. 28 73 gals. 3 qts. 60 " 2 " 40 " 1 " 240 gals, x $.17 = $40.80 65 " 240 gals. 29 150,000 gals. 4-5 = 30,000 cans., x $1.75 = $52,500. 30 4 gals. 1 pt. = 33 pts. 1 bbl. = 252 pts. . 334-252 = f bbls. 72 WEIGHTS 31 75 bbls. x 252=189 pts. -7-2 =94 qts. 1 pt. 94 qts.-:- 4 = 23 gals. 2 qts. Ans. 23 gals. 2 qts. 1 pt. 32 f bbls. x 252 = 168 pts. 13 gals. 1 pt. = 105 pts. 105-5-168= Ibbl. 33 1 of (16 gals. 2 qts.) = 33 qts. 1* bbls. X 31* X 4= 189 qts. 33 + 189 = i 34 f gaL-5-31J = &= .0238 bbl. 35 .375 bbl. x 31^= 11.8125 gals., x 4= 47.25 qts 187 Page 141 4 2.75 m. x 1.82 m. x 1.12 m. = 560.56 cu. m., x 10 = 5605.6 cu. dm., li., or kg. 5 5605.6 x 1.057 qts. = 5925. 1192 qts., -5-4= 1481.2798 gals 5605.6 x 2.2 Ibs. = 12332.32 Ibs. WEIGHTS 189 Page 145 "39 5oz.x20+5pwt. = 105pwt. 105^240=-^ Ib 40 A of rifr Ib. = ? VV= -2025 Ib. 41 .08lb.xl2=96oz.,x20=19i pwt. 43 4 oz. X20+10 pwt. = 90 pwt., -J- 240 =.375 Ib. 44 2 cen. x 100 + if Ib. = 200}| Ibs. 200ff Ibs. + 2000 Ibs. 45 3cen. xlOO+Hb. = 300Hbs. 300 Hbs.-f 2000 Ibs. = .1 5025 T CIRCULAR MEASURE 78 46 T 5 T T.x20=8cwt. cwt.xlOO=33ilbs. Ans. 8 cen., 33 Ibs., 5 oz. 47 .075T.x20 = 1.5cwt. .5cwt.xlOO=50lbs. Ans.lcwt.501bs. 48 *of2*T. = |T. A-5-f 49 .065 T. = sVV T.-7-3=sViy T. 50 17 cwt. x 100 -7-50 Ibs. = 1750 Ibs., -7-200= .875 T. 190 Page 145 3 434.28 grains x 15.4 grs. = 6687.912 grains, -7- 24 =278 pwt. 15.912 gr. = 278 pwt. -f- 20 =13 oz. 18 pwt. Ans. 1 Ib. 1 oz. 18 pwt. 15.912 gr. 6687.912 gr. -7-437 5 gr. = 15 oz. 125.412 grs. Av 4 74,625,837 grains-r 1000 = 74,625.837 li. 5 lbbl.x31x4=126qts.-7-1.057qts. = 119.20-!-li. 6 87.5 m. x 115 m. x .015 m. = 1509.375 cu. m., xlOOO= 1,509,375 cu. dm., or li. CIRCULAR MEASURE 191 Page 147 9 29 x 60 + 35' = 1775'. x 60 + 26" = 106,526" 10 943,767"-r-60= 15,729' 25". 15,729'-r60=262 9' Ans. 262 9' 25" 11 f of45=16F. FxOO=52J'. 'x60 = 30" Ans. 16 52' 30" 12 1 quad = 90, X 60x60 =324,000". 25"-r 324, 000" = r ^ quad. 74 TIME 13. ^3=^ Ans. 14 .32 quad. +4= .08 circum. 15 5 2' 3"= 18,123"; 1 40' 41"= 6041" 6041*18,123= . 16 9 3' 28"=33,948"; 25 3' 28"=90,208". 33,948*90,208 = .3763 17 $of 22 50' = 274'; 9 8' = 548'. 274'*548'=i. 18 . 125 x 60 = 7.5'. .5' x 60 = 30". Ans. 7' 30" TIME 192 Page 148 10 1 day 2 hrs. 40 min. 20 sec.*2=13 hrs. 20 min. 10 sec. 11 2 min. 35 sec. x 3= 7 min. 45 sec. 12 6x4 wks. = 24 wks. 6 x $3 = $18 weekly income, - $5 = $13. 24 x, $13 = $312. 13 5 hrs. x 60 + 15 min. = 315 min. , x 60 + 25 sec. = 18,925 sec. 14 2 yrs. X365 + 11 days=741 days, x 24 =17,784 hrs., x60+ 12 min. = 1,067,052 min. 15 3 yrs. x 365 + 37 da. = 1132 da., x 24+ 16 hrs. = 27,184 hrs., x 60+24 min. = 1,631 ,064 min., x 60 + 13 sec. = 97,863,853 sec. 16 58,967,379 sec. -7-60=982,789 min. 39 sec. ; 982,789 min.*60 = 16,379 hrs. 49 min. ; 16,379 hrs.*24=682 days 11 hours 682 da. -7-365 = 1 yr. 317 da. Ans. 1 yr. 317 da. 11 hrs. 49 , min. 39 sec. TIME 75 17 47,675imn.-r60=794lirs.35mm.;794hr6.-r24 Ans. 33 days 2 hrs. 35 min. 18 427,329 sec.^60= 7122 min. 9 sec. ; 7122 min. -r 60= 118 hrs, 42 min. ; 1 18 hrs. -5- 24 =4 da. 22 hrs. Ans. 4 da. 22 hrs. 42 min. 9 sec. 19 157,540 min. -=-60 =2625 hrs. 40 min. ; 2625 hrs.-;- 24= 109 da. 9 hrs. Ans. 109 da. 9 hrs. 40 min. 20 8,567,983 sec. -r- 60 = 142, 799 min. 43 sec. ; 142,799 min.->60 = 2379 hrs. 59 min. ; 2379 hrs. -f 24 = 99 da. 3 hrs. Ans. 99 da. 3 hrs. 59 min. 43 sec. 21 1 da. 6 hrs. 15 min. minus 21 hrs. 25 min. =8 hrs. 50 min. 8 hrs. x 60 + 50 min. = 530 min. 22 1 da. 5 hrs. 8 min. 16 sec. minus 15 hrs. 9 min. 25 sec.. = 13 hrs. 42 min. 19 sec. 23 5yrs.x365 da. = 1825 da. 1825x25 min. = 45625 min., -f- 60=760 hrs. 25 min. 760 hrs. ^24= 31 da. 16 hrs. Ans. (without leap year day) = 31 da. 16 hrs. 25 min. 24 6 mo. x 20 da. = 120 school da.,x(25 min. x 2 trips ) x 2 (return trips) = 12,120 min., -f- 60 = 202 hrs. 25 f yr.x365 = 304 da. $ da. x 24 =4 hrs. Ans. 304 da. 4 hrs. 26 1 da,:= 86,400 sec. , 2 hrs. x 60 + 30 min. = 150 min. , x 60 + 45 sec. = 9045 sec. 9045-5-86,400 = ^& da. 76 TIME 27 6 da. x 24 + 15 hrs. = 159 hrs., x 60 +40 min. =9580 min., x 60 + 36 sec. = 574, 836 sec.; 3 da. x 24 + 7 hrs.=79 hrs.,x60 + 50 min.=4790 min., x60+18 sec. = 287,418 sec. 287, 418+ 574,836 =. 28 .075x24=1.8hrs. .8hr.x60=48min. Ans. 1 hr. 48 min. .625 wk.x 7 = 4.37 J da. f da.x24=9 hrs. Ans. 4da.9hrs. .378 yr. x 365 =137.97 da. .97 da. x 24=23.28 hrs. .28 hr. x 60= 16.8 min. .8 min. x 60=48 sec. Ans. 137 da. 23 hrs. 16 min. 43 sec. 29 1 wk. = 168 hrs. 2 da. x 24 + 18 hrs. = 66 hrs. = wk. 30 .58 yr.x 365= 211.7 da. .7 da. x 24 = - 6. 8 hrs. .8hr.x 60=48 min. Ans. 211 da. 16 hrs. 48 min. 31 34 da. x 24+ 14 hrs. = 830 hrs. , x 60 + 6 min. =49,806 min., x 60+24 sec. = 2,988,384 sec. 4 da. x 24 +7 hrs. = 103 hrs.,x 60 + 45 min. = 6205 min. , x 60 + 48 sec. = 372,348 sec. 372,348-J-2,988,384= .125 32 .975yr.x365=355.875da. .875 da. x 24 =21 hrs. Ans. 355 da. 21 hrs. 33 .125 yr.x 365 = 45. 625 da. .625 da. x 24 = 15 hrs. Ans. 45 da. 15 hrs. 34 1 mo. =720 hrs. 22 da. x 24 +12 hrs. = 540 hrs. 540^-720= | mo. LONGITUDE AND TIME 77 35 1 mo. = 2,592,000 sec. 2 hrs. x60+40min. = 160 min.,x60 + 36 sec. = 9636 sec. 9636-2,592,000 = ^^ mo. 36 1 wk. = 10,080 min. 11 hrs. x 60 + 33 min. = 693 min* 693-MO,080 = ^wk. 37 1 da. = 86,400 sec. 31 min. x 60 + 30 sec. = 1890 sec. 38 4.655 yr. .655 yr.x 365 = 239.075 da. .075 da. x 24=1. 8 hr. .8 hr. x 60= 48 min. Ans. 4 yr. 239 da. 1 hr. 48 min. 39 lwk. = 168hrs. 3 da. x 24 +3 hrs. =75 hrs. 75-M68 = .4464+wk. 40 6 mo. x 30+ 9 da. = 189 da., x 24 + 13 hrs. = 4349 hrs., x 60 + 35 min. = 272,965 min., x 60 =16,377, 900 sec. ; 2 mos. x30+ 3 da. = 63 da., x 24+4 hrs. = 1516 hrs., x 60 + 28 min. = 90,988 min., x 60 +28 sec. =5,459, 308 sec. 5,459,308-r 1,637, 790=. 333+ 41 12 da. x 24+ 1 hr. = 289 hrs. , x 60x 60= 1,040,400 sec. 3 hrs. x 60 +37 min. = 217 min., x 60 + 1 sec. =13,021 sec. 13,021 -5-1 ,040,400 = .0125 + . LONGITUDE AND TIME 193 Page 150 8 2 hrs. 25 min. 6 sec., x 15 = 30 16' 30" 9 1 " 24 " 16 " x 15 = 21 4' 0" 10 3." 14 " 28 " x 15 = 48 37' 0" 78 CIRCULAR MEASURE 11 5hrs. 13min.l2sec.,xl5 = 7818' 0" 12 4 " 8 " 12 " x 15 = 62 3' 0" 13 17" 9 " 14 , x 15 = 257 18' 30" 360 - (257 18' 30") = 102 41' 30" 14 15 hrs. 14 min. 13 sec., x 15 = 228 33' 15" 360 - (228 33' 15") = 131 26' 45" 15 122 24' 15" - 93 56' = 29 19' 15" ~ 15 = 1 hr. 57 min. 17 sec. 16 90 5'- 74 3"= 16 4' 57",-M5 = l hr. 4 min. 19f sec. 17 72 53' - 13 23' 53" =59 29' 7",-M5 = 3 hrs. 57 min. 56 T V sec. 18 122 24' 15"- 74 3"=48 24' 12". -5- 15 = 3 hrs. 13 min. 36| sec. 19 87 37' 30"+ 30 18'= 117 55' 30", -5- 15 = 7 hrs. 51 min. 42 sec. 20 99 5' - 90 15' 16" = 8 49' 44", 4- 15 = 35 min. 18}| sec. 21 84 26'-77 2' 48"=7 23' 12", -5-15 = 29 min. 32$ sec. 22 166 28' 54" E + 73 34' W= 190 2' 54" 360- 190 2' 54" = 169 57' 6"-M5 = ll hrs. 19 min. 48 sec. 23 122 24' 15"+2 20' 22" = 124 44' 37", -5- 15 = 8 hrs. 18 min. 583*5 sec. P. M. 24 71 3' 30" W. + 116 28' 54" = 187 32' 24", -5- 15 = 12 hrs. 30 min. 9fsec. 6 P. M. + 12hrs. 30 min. 9f sec. = 6 hrs. 30 min. 9| sec. A. M. next day. 25 30 18'- 2 20' 22" =27 57' 38", -5- 15 = 1 hr. 51 min. 50 r 8 5 sec. A. M. next day. CIRCULAR MEASURE 79 26 10 hrs, 30 min. - 7 hrs. 20 min. = 3 hrs. 10 min. , x 15 = 47 30'. 47 30' + 121 26' = 168 56' W. 14 hrs. 25 min. - 10 hrs. 30 min. = 3 hrs. 55 min. x 15 - 58 45'. 121 26' - 58 45' - 62 41' E. 13 hrs. 10 min. - 10 hrs. 30 min. = 2 hrs. 40 min. , x 15 = 40. 121 26' -40 = 81 26' W. 10 hrs. 30 min. -5 hrs. 15 min., 5 hrs. 15 min.,xl5 = 78 45', + 121 26'= 200 11'. 360 - 200 11'= 159 49' E. 27 15 hrs. 30 inin. - 7 hrs. 30' = 8 hrs. , x 15 = 120. 120 -73 32' = 46 28' E. 28 26 hrs. - 16 hrs. = 10 hrs. , x 15 = 150. 150 + 2 20' 22" = 152 20' 22" E. 29 25 hrs. 25 min. -13 hrs. 25 min. = 12 hrs., x 15 -180. 180 - 71 3' 30" - 108 56' 30" E. 30 18 hrs. 30 min - 9 hrs. 25 min. = 9 hrs. 5 min., x 15 = 136 150 136 15' - 2 20' 22" = 133 54' 38" W. 31 8 hrs. 15 min. -7 hrs. 30 min. = 45 min., :: 15 = 11 15'. 95 56' -11 15'= 84 41' W. 32 26 hrs. 15 min. - 23 hrs. 45 min. = 2 hrs. 30 min., x 16= 37 30'. 73 34' -37 30' =36 4' W. 33 ' 5 hrs. 5 min. 21f sec. , x 15 = 76 20' 25". 76 20' 25" - 2 20' 22" = 74 3" W.- New York. 34 6min. 6* sec.,x 15 = 1 31' 37i", + 71 3' 30" = 72 35' 7J" W. 80 ADDITION OF COMPOUND NUMBERS 35 122 24' 15"- 74 3" =48 24' 12",-;- 15 = 3 hrs. 13 min. 36f sec. 3 A.M. + 3 hrs. 13 min. 36f sec. = 13 min. 36f sec. past 6 A.M^ 36 37 min. x 15 = 9 15'. 74 3" - 9 15'= 64 45' 3" W. 37 11:25 P. M. - 5:20 P. M. = 6 hrs. 5 min., x 15 = 91 15'. 91 15' -30 18= 60 57' W. ADDITION OF COMPOUND NUMBERS 194 Page 158 1 69 rds. 2^ yds. 1 mi. 14 2 2 ft. 3 in. 16 9 25 11 1 mi. 125 rds. 3yds. 2 ft, in. 2 7yds. 2ft. 5 It 2 9} in. 3 1 6* 41 2| 22 vds. 1ft, 4 in.= 22 yds. 1ft. 10 in. 3 25 yds. 1ft 9 in 32 1 8 35 6 4 7 2 11 9 106 yds. 8 =19 rds. 1 yd. 2 ft. 2 in. 4 23 mi. 118 rds. Oyds. 14ft. 19 137 11 8 62 Sin. 23 147 6 9 7 74 mi. 96 rds. 2 yds. Oft. Sin. ADDITION OP COMPOUND NUMBERS 81 10 11 22 rds. 2 yds. 18 4 22 6 16 2ft. 2 1 4 Oin. 3 80 rds. 4yds. 7 mi. 59 rds. 8 96 5 9 26 87 Oft. Oyds. 3 in. 6 ft. 7 in. 7 8 8 8 3 46 mi. 252 rds. 46 mi. 252 rds. 71 mi. ' 23 rds. 9 17 23 Hvds. 2 yds. 4| yds. 2 3 2ft. 2in.= ft. 8 in. ft. in. 2 9 103 mi. 41 rds. 103 mi. 41 rds. 1J yds. ft. 3 in 24 3|- 4 yds. 5 yds. 2^ ft. 9in.= ft. Sin. Oin. 3 6 9 2J yds. 21- ft. 7 in 3 14 Jyd.=0yd. 1ft. 2 2 6 in. 3 3 3 yds. 1 ft. fmi.=240rd. Oyd. [|rd. = 2 ff y t.' = Oft. 2 1 240 rds. 3 yds, 79 chs. 3 rds. 65 2 33 2 46 1 75 , 1ft. 161. 11 6 13 2 6 in. 3 mi. 60 chs. 1 rd. 23 1. OF THE UNIVERSITY 82 ADDITION OF COMPOUND NUMBERS 12 75 A. 4 sq. rds. 9 sq. yds. sq. ft. 72 sq. in. 27 48 18 92 7 100 29 8 139 7 129 109 A. 154 sq. rds. 2J sq. yds. 2 sq. ft. sq. in. 109 A. 154 sq. rds. 3 sq. yds. 6 sq. ft. 72 sq. in. 13 A. = 80 sq. rds. f sq. yds. = 5 sq. ft. Ans. 80 sq. rds. 5 sq. ft. 14 f A.= 96 sq. rds. sq. yd. sq. ft. f sq. rd. = 13 4 | sq. yd. = 6 96 sq. rds. 14 sq. yds. 1 sq. ft. 15 5 cds. 7 cd. ft. cu. ft. 2 2 12 7f 6 15 30 2 19| cds. Ocd. ft. 13 cu. ft.= 19 cds. 3 cd. ft. 13 cu. ft. 16 95 cu. yds. 26 cu. ft. 985 cu. in. 87 19 876 98 3 875 281 cu. yds. 22 T V cu. ft. 17 29 gals. 2 qts. 1 pt. 16 3 11 1 49 gals. 1 qt. 197 qts., X $.16 =$19.70. 18 5825 pts. + 4285 pts. + 3426 pts. = 13,536 pts. 13,536 pts.-J-2-6768 qts.,x$ = $846. 6768 qts. -=-8 = 846 pks.,^4 = 21U bu. ADDITION OF COMPOUND NUMBBBS 83 19 Ibu Opk 4qts. 1 pt. 231 27 I 2 bu. 2 pks. 3 qts. 1 pt. = 83 qts. 20 9 hrs. 15 min. 8 20 11 10 35 9 45 6 50 55fhrs.,x $.35 = $19.51*. 21 2 gr. 1 doz 3 units. 3 20 354 5 gr. 11 doz. 3 units. 22 2 bdls. 1 rm. 3 qrs. shts. 3 17 1 010 6 bdls. Irm. 4 qrs. 17shts. = 6353 shte. 23 6 17 s. 5 d. 7 11 4 973 23 16s. Od. = 23f,x$4.86=$115.67. 24 CO cts. + 10 cts. + 137| cts. + 95 cts. + 25 cts. = $3. 25 14 T. 13 cwt. 75 Ibs. 25 12 26 2 5 14 17 16 29 60 T. 7 cwt. 44 Ibs. 84 SUBTRACTION OF COMPOUND NUMBERS 26 84 T. 12 cwt. 74 Ibs. 6 ozs. 23 12 26 8 51 16 45 15 81 5 4 7 241 T. 6 cwt. 51 Ibs. 4 ozs. 27 51bs. 9oz. 14pwt. 3 7 13 2 4 11 11 Ib. 9oz. 18 pwt. SUBTRACTION OF COMPOUND NUMBERS. 195. Page 160 25 A. 74 12 74 sq. rds. 40 117 112 A. 71 sq. rds. 160 A. - 112 A. 71 sq. rds. = 47 A. 89 sq. rds. 7 mi. 3 , 25 rds. 110 3 yds. 4ft. 2 6 in 3 mi. 3 mi. 234 rds. 234 rds. 4* yds. 5 yds. 2ft.= Oft. (14 chs. 43 1.) x (17 chs. 25 l.) = 248.91| chs. (8 chs. 11 1.) = 15 chs. = 121.65 chs. 248.911 chs. - 121.65 chs. = 12 A. 7.26| chs. 48 cu. yds. 28 12 cu. ft, 24 1236 cu. in. 1500 19 cu. yds. 14 cu. ft. 1464 cu. in. 4 gals. 2qts. 3 Opt. 2 gals. 2qts. 1 pt. SUBTRACTION OF COMPOUND NUMBERS 85 6 31 gals. + 30 gals. lqt. = 61 gals. 3 qt. 6 gals. 2 qts. 5 3 5 2 7 3 28 53 gals. 2 qts. = 53^ gals., x $.27=$14.44i 61 gals. 3 qts. - 53 gals. 2 qts. = 8 gals. 1 qt. 7 cwt. Ib. 11 oz. 6 37 7 13 cwt. 39 Ibs. 2 oz. 11 79 8 1 cwt. 59 Ibs. 10 oz. 8 .625 Ib. x 12=7.50 oz. - 4.25 oz. = 3.25 oz. 9 T V of 72 Ibs. 12 oz. = 6 Ibs. 1 oz. 100 Ibs. - 6 Ibs. 1 oz. = 93 Ibs. 15 oz. 10 1 Ib. 2 oz. 5 pwt. 11 17 gr. 18 2 oz. 7 pwt. 6 gr. 11 2 Ibs. Ooz. 9 Odr. 1 Osc. 2 Ogr. 7 lib. 2oz. 6 dr. Osc. 13 gr. 12 5 yrs. 3 2 mos. 3 2 wks. Ida. 4 7 hrs 3 2 yrs. 2 mos. Iwk. 4 da. 4 hrs. 13 3 mos. wks. 2 Oda. 4 Ohrs. 8 min. sec. 19 29 2 rnos. Iwk. 2 da. 15 hrs. 40 min. 31 sec. 14 31 Jan. + 28 Feb. + 31 Mar. + 30 Apr. + 31 May + 30 June = 181 days. 6 Dec. + 31 Jan. + 28 Feb. +31 Mar. + 30 Apr. + 31 May + 30 June + 4 July = 191 da. , - 181 da. = 10 da. Ans. 86 SUBTRACTION OF COMPOUND NUMBERS 15 2 wks. 3*- da. -.659 wk. = l wk. 6 da. 5 hrs. 17 min. 16.8 Sec. 16 $40.25 + $21. 375 + $70.50 +$11.64 + $7.50 + $8.25 + $16+ $38 + $85.914+ $107.393= $406.822. $729 - 406.822 = $322.178. 17 | of 3} mi. = ifmi. + 17 1 rds. = 314^ rds. 314| rds. - 120* rds. = 193 rds. 5 yds. 8} in. 18 184 da. - 180 da. = 4 da. , x 24 = 96 hrs. x 60 = 5760 min. , x 60 = 345,600 sec. 19 Sec. -v- 3 = 32 yrs. 3 mos. 3 wks. da. 37 hrs. 24 min. 5J sec. Fst.x4=12 2 1 6 12 48 28 20 yrs. 1 mo. 1 wk. 1 da. 4 hrs. 35 min. 37;|sec. 20 |ofFirst=6T. 12 cwt. 18 T 9 ^ Ibs .25 T. = 5 6 T. 7 cwt. 18& Ibs. 21 T 2 r sq. rds. =5| sq. yds., - f sq. yd. = 4f sq. yds. 22 48 17 s. 6 d. 2 far. 39 14 9 3 9 2s. 8 d. 3 far. 23 55 58' 40" - 34 22' = 21 36' 40" 24 ft Ib. x 12 = T % oz., x 20 = 18 pwt. 5 Ibs. 4 oz. 8 pwt. - 18 pwt. = 5 Ibs. 3 oz. 10 pwt. 25 JB-g- = llB.lJd. |of|s. = 6d. 11 s. IJd- -6d. = 10s. 26 46 ft. x 46 ft. = 2116 sq. ft. , - 46 sq ft. = 2070 sq. ft. MULTIPLICATION OF COMPOUND NUMBERS 87 MULTIPLICATION OF COMPOUND NUMBERS 196 Page 161 1 5 mi. 28 rds. 3 yds. 2 ft. 11 in. 9 45 mi. 258 rds. 2 yds. 2 ft. 3 in. 2 79 chs. 3 rds. 23 1. 7 6 mi. 79 chs. 3 rds. 11 1. 3 158 8q. rds. 270 sq. yds. 7 sq. ft. 138 sq. in. 11 10 A, 148 sq. rds. 4 sq. yds. 2 sq. ft. 6 sq. in. 4 98 cds. 13 cu. ft. 758 cu. iu. 13 1275 cds. 46 cu. ft. 1214 cu. in. 5 5 bbls. 29 gals. 3 qts. 23 136 bbls. 22i gals. 1 qt. = 136 bbls. 22 gals. 3 qt. 6 7 oz. 17 pwt. 23 gr. 96 63 Ibs. 2 oz. 4 pwt. gr. 7 75 cwt. 15 oz. x 274=1027 T. 12 cwt. 56 Ibs. 14 oz. 8 9 yrs. 7 mos. 3 wks. 5 da. 19 hrs. 35 min. 28 sec 63 608 yrs. 9 mos. 1 wk. 2 da. 10 hrs. 14 min. 24 sec. I 9 17 rds. 3 yds. 2J ft. 4 70 rds. 4 yds. ft. 4 in. 88 DIVISION OF COMPOUND NUMBERS 10 7 cwt. 29 Ibs. 4 oz. 9 3 tons 5 cwt. 29 Ibs. 4 oz. = 6563^ Ibs. 6563ix$.09|= $623.51. 11 5 mi. 19rds. 4yds. 54 273 mi. 105 rds. 1 yd. 1 ft. 6 in. 12 13x365 + 3 days = 4748 days, x $.25 = $1187. 4748 pts.-=-2 = 2374 qts.,-=-4=593 gals. 2 qts. 593 gals.-r3H=18bbls. 26 gals. Ans. ISbbls. 26 gals. 2qts. 13 $1 ,25 x 12 x 13 = $195 cost :f milk. $1187 - 195 x $992. 14 $1375-r$125 = ll. 5 A. 24 sq. rds. 19 sq. yds. 7 sq. ft 11 56 A. Ill sq. rds. 5 sq. yds. 5 sq. ft. 56 A. Ill sq. rds. 5 sq. yds. 7 sq. ft. 36 sq. in. 15 5 pwt. 6 gr. x!7 = 4 oz. 9 pwt. 6 gr. DIVISION OF COMPOUND NUMBERS 197 Page 162 1 9) 9 mi. 78 rds. 4 yds. 2 ft. 8 in. I mi. 8 rds. 4 yd. ft. 7f in. 2 6) 68 chs. 2 rds. 24 1. II chs. 1 rd. 20f 1. 3 16) 296 sq. rds. 29 sq. yds. 8 sq. ft. 98 sq. in. 18 sq. rds. 16 sq. yds. 8 sq. ft. 141 J sq. in. DIVISION OF COMPOUND NUMBERS 89 4 28) 97 cds. 11 cu. ft. 979 cu. in. 3 cds. 59 cu. ft. 1454|i- cu. in. 5 19) 23 bbls. 28 gals. 5 qts. Ibbl. 8 gals. qts. 1 T V ptfl. 6 15) 56 Ibs. 11 oz. 19 pwt. 21 gr. 31bs. 9oz. llpwt. 23fgr. 7 95) 87 cwt. Ib. 13 oz. cwt. 91 Ibs. 9f oz. 3 17) 24 yrs. 11 mos. 2 wks. 3 days 11 hrs. 47 min. 1 yr. 5 mos. 2 wks. 3 days 11 hrs. 59 min. 14^ sec. 9 20,600 Ibs. -f- 294 = 70 T W Ibs. 10 340 Ibs. 11 oz. ^ (2 x 54) = 6 Ibs. 4} ozs. 11 6 mi. sq. = 36 sq. mi. , x 640 = 23,040 A. 23,040 A. 4- 62 =371 A. 6 sq. chs. 2 sq. rds. 40^ sq. 1. 12 39 sq. rds. x 301 + 2 sq. yds. = 1181f 'sq. yds. , x 9 + 6 sq. ft. = 10,641 1 sq. ft., x 144 + 128 sq. in. = 1,532,540 sq. in. 1,532,540 sq. in.-f-2210 in. = 693^1 in., width. 693|f 1 in. = 3 rds. 2 yds. 2 ft. 3jft in. Ans. 13 120 cu. yds. 5 cu. ft. -r (5x4) = 6 cu. yds. 432 cu. in. or 162 cu. ft. 432 cu. in. 14 2 gals, x 4+ 3 qts. = 11 qts., x 2 + 1 pt. = 23 pts. 23pts.x2 = 46half pts. 15 5280 f t. 4-30= 176, x 2 = 352 rails, 90 REVIEW OF COMPOUND NUMBERS REVIEW OF COMPOUND NUMBERS 198 Page 163 1 2 hrs. 55 min. = 175 min. 1 75 x 59 x 4^ ft. = 45,602 T V ft. 45,602^ ft.-f-5280=8 mi. 3362^ ft. 3362 T V ft.-^3 = 1120 yds. 2& ft. 1120 yds.-r-Si = 203 rds. 3 yds. 8 mi. 203 rds. 3| yds. 2 T V ft. = 8 mi. 203 rds. 4 yds. 7 in. 2 Imi. 8 rds. = 328 rds., x 16^ = 5412 ft. 5412 ft. x 3 ft. x 2 ft. = 32,472 cu. ft. 32,472 cu. ft. -=-27 = 1202 cu. yds. 18 cu. ft. 2 Metric. 1649.58 m.x .914 m.x 609 m. = 918.19911708 cu. m. or steres. 918. 19911708 steresx 1.308 cu. yd. = 1201. 004 cu. yd. 3 855.95-r 1.50 = 570 cwt. 63J Ibs. 4 11 min. 45 sec. = 705 sec. 11 hrs. = 39, 600 sec. 4 Metric. 1609.34 m. x 56 R r = 90,396.97. 5 3 ft. 2 in. = 38 in. ; 2 ft. 10 in. = 34 in. ; 38 in. x 34 in. x 5 in. = 6460 cu. in. 1 ft. 4 in. = 16 in. ; 3 ft. = 36 in. 16 in. x36 in. x 5 in. = 2880 cu. in. 6460 cu. in. + 2880 cu. in = 9340 cu. in. ,-7-1728=5 cu. ft. 700 cu. in. 5 Metric. .965 m. x .863 m. x. 127 rn. = . 105764965 cu. m. .406 m. x .91 m. x 127 m. = .04692142 cu. m. .105764965 cu. m. + .04692142 cu. m. = .152686385 cu. m. 6 3 ft. x 2 ft. x 2= 14 sq. ft. 2J ft. x 1 X 2 = 4| sq. ft. 3 ft. X 1 ft.x2 = 6sq. ft. 14 sq.ft. + 4| sq.ft. + 6 eq. ft. = 24j sq. ft., surface of second block. 4 ft. x 4 ft. x 6 = 96 sq. ft. , surface of first block. 96 sq. ft. + 24 sq. ft. = 1203 sq. ft. REVIEW OF COMPOUND NUMBERS 91 7 640 A. x 160 = 102,400 sq. rds.,x 30 | = 3,097,600 sq. yds.,x9 = 27,878,400 sq. ft.,x!44 = 4,014,489,600 sq. in. 7 Metric. 640 A. ^2.47 A. = 259.10921 hectares. 8 16ft.x5ft.x3|ft. = 280cu. ft., -f- 128 = 21 f cd. 8 Metric. 4.87m. x 1.06m. x 1.52m. = 7.846544 cu. m. or steres 9 9| A. x 160 = 1560 sq. rds., -^ 260 = 6 rds. 10 16 pwt. 11 grs. =395 grs. 5 Ibs. 1 pwt. 11 grs. =28,835 grs. 28,835 -r 395 = 73. 10 Metric. 1872.4 gr.-f- 25.649 gr. = 73 spoon, (23 gr. remaining). 11 7 yrs. mo. wks. da. hrs. min. sec. _ 1 _ 2 __ 3 11 35 42 6 yrs. 10 mos. 1 wk. 3 da. 12 hrs. 24 min. 18 sec. 12 (480 rds. + 330 rds.) x 2 = 1620 rds., x!6 = 26,730 ft.,-j-24f = 108. 108postsx$.12 = $135. 13 1620 (rds.) x 3x 1-J Ibs. = 7290 Ibs., x $.05 J = $400.95. 14 32 gals, x $.17 = $5.44 cost. 32gals. -(. 06^x32) = 30 gals. 15 gals. x$. 29 = $4. 35; 5 gals. x $.27 = . $1.35. 8| gals, x $.26= $2.27 J; IJgals. x$.28 = $.35. $4.35 + $1.35 + $2.27^ + $.35 = |8.32J. selling price $8.32J S. P. - $5.44 0. = $2.88} profit. 15 660 ft. ^5280 ft. = =.125 mi. 16 4x$31.75 = $127. $127 + $175 + $17.50 + $18.42=$337.92. $337.92^$1.50 = 225.28 centals. 92 HE VIEW OF COMPOUND NUMBERS 17 91 cd. + 7 cd. = 16| cd., x 128 = 2144 cu. ft. 8964 cu. ft. - 2144 cu. ft. = 6820 cu. ft. 6820 cu. ft.-M28 = 53& cd. 53& cd. x $7. 25 = $386.29. 17 Metric. 33.514492 steres + 27.173913 steres = 60.688405 steres. 253.736413 steres - 60.688405 steres =193.048008 steres. 193.048008 steres. x $2.001 = $386.289. 18 7 mi. 148 rd. x 365 = 2723if mi. 18 Metric. 1609.372 m.x 365 = 587, 420.78 m. 19 |lb.= 9oz. 12pwt. Ogr. 4foz.= 4 -16 16 3Hpwt.= 31 8 1 Ib. 4 oz. pwt. gr. 1 Ib. 4 oz. - 11 pwt. 3 gr. = 1 Ib. 3 oz. 8 pwt. 21 gr. 20 2 Ib. x!2+6 oz. = 30 oz.,x20+17 pwt. = 617 pwt.,x24 + 12 gr. = 14,820 gr.-r 25.8, = $574.41. 20 Metric. 961.5584 grs. -r 1.6753 grs. = $573.96. 21 320 rds.-r!2 = 26f rds. to block, x 16^ = 440 rds. 6 yds. 2} cu. ft. x 440 = 2680 cu. yds. 20 cu. ft. 22 6 gals, x 8=48 pts. x 9 = 432 pts. 35 pts. + 96 pts. + 276 pts. + 11 $ pts. = 13| Pts. = 6 qts. 11 pts. 23 161 ft. x 6 ft. x 1 ft. = 90.75 cu. ft. 24 10 x 43560 sq. ft. = 435,600 sq. ft. , x f = 326,700 * (45 x 150= 6750) = 48* lots. REVIEW OF COMPOUND NUMBERS 93 25 24x(ll pwt. 3 gr.) = 264pwt. 552 gr. = 14 2 V oz.,x $1.60 = $22.96. 25 Metric. 24x18.636 gr. = 447.264 gr.,-j- 31.168 gr. = 14.35 spoons, x $.50= $7.17-}. \ 26 98 bbl. x 31 J gal. = 3087 gal. , x (6 - 4) = 1543 min. 1543| min. = 1 da. 1 hr. 43 min. 30 sec. 27 Quarter Section. = 160 A. x 160 = 25,600 sq. rd. - (17x17 sq. rd.) = 25,311 sq. rd. = 158 A. 31 sq. rd. 28 15 ft. 4- 8 ft. = 11 cd.,x $9.75 = $18.28. 29 8 J- ft. -f- 3 ft7= 2| ft. 5280 ft. -^8| = 640 revolutions of large wheel. 640 x 2|= 1760 revolutions small wheel. 1760 -640 = 1120 times. 30 *A. = 80sq. rd. sq. yd. sq. ft. sq. in. 79 _ 7 _ 1 6 _ 98 _ 22J- sq. yd. 2 sq. ft. 46 sq. in. = 22 sq. yd. 4 sq. ft. 82 sq. in. 31 27 ft. = 9 yd., 4-f = 12 strips. 12 ft. = 4f yds. 12 x4| yds. = 56 yds. 32 (15 ft. + 111 ft.) x 9 ft. x 2 = 472} sq. ft. sides. 15 ft. x 111 ft- = 168f sq. ft. ceiling. 641]- sq. ft. sides and ceiling. 6| ft. x 3 x 2 = 40 sq. ft. doors. 2 ft. x 6 X 3=39 sq. ft. windows. 79 -r-2 = 39 1 sq. ft. allowance. 6411 sq. ft. -39sq. ft. = 601| sq. ft.,-r-9 = 66| yds. x $.32 = $21.395. 94 REVIEW OF COMPOUND NUMBEKS 33 9Ht.x6|ft.x4ft. = 278Hcu. ft. 34 i of First =1 A. 79 sq. rd. 21 sq. yd. 8 sq.ft. 13 sq. in. 100 24 7 96 138 sq. rd. 27i sq. yd. sq. ft. Gl sq. in. = 138sq.rd. 27 sq. yd. 2 sq.ft. 99sq.in. 35 118 18' 00' Los Angeles. 87 _ 37 _ 30 Chicago. 15 )30 40' 30" 2hrs. 2min. 42 sec. 10 hrs. - 2 hrs. 2 min. 42 sec. = 7 hrs. 57 min. 18 sec.A. M. 36 58 22' W. 18 28 E. 15) 76 50' 5 hrs. 7 min. 20 sec. 6 hrs. 30 min. 11 hrs. 37 min. 20 sec. A. M. 37 9x24=. 375 38 |mi. = 200rd. Oft. in. rd. = 5 6 f ft. = 10 200 rds. 6 ft. 4 in. 38 Metric. 1005.84 m. + 1.67 in.+ .25 m. = 1007.76 m. Ans. 39 7 ft. x 4 ft. =28 sq.ft. 105 cu. ft.-r-28 sq. ft. = 32 ft. 40 (16 ft. + 22 ft.) x 2f ft. X 2 = 215J sq. ft. 4^ ft. X 2f ft. X 3 = 4Hf sq. ft. 215} sq. ft. - 41 ^ sq. ft. = 173|| sq. ft.,x$.06 = $10.4U. 41 ^ yds. -f- f = 9^ = 10 strips. 18ft. = 6yds. 10x6 yds. =60 yds. REVIEW OF COMPOUND NUMBERS 95 41 Metric. 5.48m.x6.70m. = 36.716sq.m.-7-.68m. = 53.994ui. 42 11 ft. 11 in. = -W- yd- = 3 M yd- = 4 strips. 17 ft. 10 in. - Wyd. -W 7 - yd. x 4 = 23f yd. 43 60 ft. = 20 yd. 80ft. = 26fyd. 24 ft. = 8 yd. 20 ft. =6} yd. 36 ft. = 12 yd. 20 strips x 36| yd. =533 J yds. 8 strips x 6| yd. = 53 J yd. 12 strips x 6f yd. = 80 yds. 533 yd. + 10 yd. + 53 j- yd. + 80 yd. = 676f yd. , x $1.50 = $1015. 44 2xl701b. = 3401b.xl2 = 4080o/. $37004-4080 =$.906. 45 26 ft. -2 ft. (border) = 24 ft. = 8 yd. 8 yd. -T-$ yd. = 11 strips. 17 ft. -2 ft. (border) = 15 ft. = 5 yds. xll + ii matching = 55Hyds. (26 ft. + 17 ft.)x2 = 86 ft. = 28f yds. edging. 55H yds. + 28f yds. = 84H yds. X $1.95 = $209. 04. 46 1 mi. = 1760 yd. Htf = *. 47 f of .225 mi. = .18 mi.x320 = 57| rd. | rd. x 16J = 9 T V ft. A ft. x 12 = lOf in. Ans. 57 rd. 9 ft. lOf in. 48 fcd. ft.-r-8 = Acd. 49 (22 ft. + 16 ft.) X 9 ft. x2 = 684 sq. ft.,-f-9 = 76 sq. yd.-20sq. yd. = 56 sq. yd. 8 yd. x 1 J f t. = 4 sq. yd. to roll. 56 sq. yd. -7-4 sq. yd. = 14 rolls, x$.87= $12.25. 50 2 T. 7 cwt. 28 Ib. =4728 Ib. 5 cwt. 91 Ib. = 591 Ib. 51 396 sq. rd. 21 sq. yd. = 2 A. 76 sq. rd. 21 sq. yd. = 2^ A. X $605 - $1500 Offered. 16 x $175 = $2800 Received. $2800 -$1500 = $1300. 360 ft. -5-8 =45 ft. wide. 96 UNITED STATES MONEY 22 $16^ T L = 23 $48.75-r = 39 books. 24 874 x T V = $54.62 . UNITED STATES MONEY 199 Page 169 35 $357-5- 12f = 28 T. 26 84 x| = . $10.50. 27 648x1 = $81 .00. 28 $19-H = 1521b. 29 976 xf =$732. 30 879 X If =$1230.60. 31 $40^-| = 45f yd. 32 $9-i-$ = 14 chickens. 33 376x$|=$141. 34 $32-5-^=512 baga 36 7 37 18 xlj = $22.50. 38 189 x,^ = $63. 39 $261-5-1 = 43 Ibs. 40 $95-f-$4| = 20 sheep. 41 408x$li=$765. 42 248x$lf = $403. 43 1 00 ^-| = 114 rolls. 44 249x$2=$664. 45 726x$| = $605. UNITED STATES MONBY 97 46 97.856 M.x $19= 1859.264. 47 785.469 M. x $8 = $6283.75. 48 98.56 cwt. x $6 =$591.36. 49 7643.98 cwt. x $2| = $1 8,345.55. 50 439.86 cwt. x $.70= $307.90. 51 $95^-$lJ = 76cwt. 52 75.43 cwt. x $2 J = $188.575. 53 98, 756 lb. = 49.378 T.,x $12 = $592.54. 54 8-M2 = i 55 1975 Ib. + 1125 Ib. + 1240 Ib. = 4340 Ib. 4340 Ib.-f- 2000 = 2.17 T.,x$12f =$27.67. 56 1 Ib. Troy = 5760 gr. 25.8 gr. - ( T V of 25.8)= 23.22 gr. 5760-23.22 gr. = 57 (412.5 gr.- T V of 412.5 gr.) = 37H 5760gr.-r37Hgr. = 58 71b.xl2 + ll oz. = 95 oz., x 20 + 18 pwt. = 1918 pwt.,x 24 + 3 gr. = 46,035 gr.,-5-371J gr. = $124. 59 1 Ib. = 12 oz., x 20 + 1 pwt. = 241 pwt. , x 24 + 21 gr. = 5805 gr. 5805gr.-^23.22gr. = 60 2 Ib.xl2 = 24 oz.,x20 + 3 pwt.=483 pwt.,x24 + 18 gr.= 11,610 gr. 11,610 gr. 4- 23.22 gr. = $500, -MO = 50 eagles. 98 GENERAL ANALYSIS 61 6 Ib.xl2 = 72 oz.,x20 + 6 pwt. = 1446 pwt. x 24+18 gr.= 34,722 gr. of 385.8 - T V of 192.9 = 173.61 gr. 34,722 gr.-r-173.61 gr. = 200 half dollars. 62 llb.x!2 + 6 oz. = 18oz.,x20 + l pwt. = 361 pwt., X 24 + 16 J gr. = 8680 J gr. of 385.8 - T V of 96.45 = 86.805 gr. 8680.5 gr. -7-86.805 gr. = 100 quarters. 63 3 Ib.xl2 = 36 oz.,x20+3 pwt. = 723 pwt, x 24 + 9 gr.= 17,361 gr. T V of 385.8 gr.- T V of 38.58 gr. = 34.722 gr. 17,361 gr. -7-34.722 gr. = 500 dimes. 64 9 lb.x!2 + 2 oz. = 110 oz., x 20 + 8 pwt. = 2208 pwt., x 24= 52,992 gr. 52,992 gr. x .975 = 51,667.2 gr. pure silver. 51,667.2 gr.-r 173.61 gr. = 297.6 half dollars. 65 3 lb.x!2+8 oz. = 44 oz.,x20+ll pwt. = 891 pwt., x 24= 213,840 gr. 2* x 258 gr. - T V of 64.50 = 58.05 gr. 213,840 gr.-j-58.05 gr. = 368^ pieces. GENERAL ANALYSIS 200 Page 173 1 18: 30:: 45: (75); or, fx30 = $75. 2 15 : 7 : : 15 : (7) ; or, 15 x ^=7 days. 3 48 : 84 : : 108 : (189) ; or, VJT x 84= $189. 4 24 : 22 : : 564 : (517) ; or , A& 4 x 22 = 517 mi. 5 160 : 175 : : 96 : (105) ; or, ^ x 175= 105 T. GENERAL ANALYSIS 99 6 50: 18:: 75: (27); or, ^x 18=27 A. 7 112.50 : 90 : : 50 : (40); or, TT 5 T ^ x 90=40 chairs. 8 8|: 12*:: 17.50: (25); or, 17.50x/ 5 x^=$25. 9 78 : 58 J : : 12 : (9) , or, if x ip=9 men. 10 24 : 32 : : 18 : (24); or, 18 x f = 24 men. 11 18 : 42 : : 61.20 : (142.80) ; or, ^ j 2JL X 42= $142.80. 12 30 : 100 : : 3.75:(12.50) ; or, A^Px 100 =$12.50, 13 12: 10:: 14: (llf); or, 14x12 = llf days. 14 12 r 22 : : 486 : (891) ; or, V x 22= $891. 15 486 : 891 : : 12 : (22) ; or, ^ x 891 = 22 cows. 16 44i: 33J:: 9\ : (7i); or, Vx^r* 4 A =7J yda. 17 480J 30o} : :720: ( 562 - 50 )5 or ' 720 xHx|^= $562.60. 18 l ::640: ( 36 ) ; or ' 19 130 : 80 : : 117 : (72) ; or, {ft x 80= $72. 20 108 : 81 : : 120 : (90) ; or, 120 x 81-M08=90 horses. 21 si l l} ::12: (18); or, 12 x V x f = 18 days. 22 1.90: S80 : :20: (4000) ; or, T 3fr* 380 = 4000 lbs ; 23 1:|::27:(20J); or, 27 x f = 20J yd? 100 GENERAL ANALYSIS 24 9J: :11.40:{20); or, 11.40x T i VxfxlOxf=$20. 25 60 . ::12:(24);or, VxUx9 = 24days 26 4J:3|::12:(9);or, 12xfx^ = 9 brooms. 27 42 : 35 : : 6 : (5) ; or, ^x 35 = 5 men. 10:7 1 28 28:25 V : :2: (1); or, 2x Ax T Vx,M=l day. 10:8 J 30 11 J: 10J:: 3.45: (3.15); or, 3.45x^ T x ^ = $3.15. 31 10 J : 8| : : 121 : (10&) ; or, 4 ^ x 2 2 i x V L = W? ft - = !0 ft. 2J in. 32 5 T $ i : 3J : : 16J- : (10); or, V x if x V = 10 ft. 33 MLiw-ai ::3J:(14);or, ^ XT\X VX ^^ = 14 days. 36:44 34 22:14l::24:(32); or, 3*x j|x V x 12=32 gal. 6:44) 2:14l::24:(32); 7:12j 35 i| : : : 198 :(238) ; or, 198 x jf x | = $238. 36 14 Ibs. : 2072 Ibs. : : 1 : (148) ; or, & x 2072 =$148 37 7x5x|-r.l5 = 87j doz. 38 . 717 M x 15-r .045 = 239 Ibs. 39 150 X }$$ X 1.20^. 07 J = 3000 sacks. 40 3x60x T V=84 weeks. 41 12xl.75 = $21; 80x.01} = $l. 21-^1 = 21 sacks. PARTNERSHIP 101 PARTNERSHIP 201 Page 178 1 $2500 +$1500 = $4000. A's share=, or f of $1840=$1150. B's " =J$, or | of $1840=$ 690. 2 H-tV=AB J SBhare. & of $637 =$245 A's loss. T 8 T of $637 = $392 B's loss. 3 40 x 11 = 440. A's share $f of $96 = $44. . 65x 8 = 520. B's " f| of $96 = $52. 960. 4/ $2892 -$964 =$1928, sec. gain. $& of $6000 = $2000 inv. 1. 6000 - 2000 = $4000 inv. oth. 5 $2000 x 1 2 = 24,000. f , or & of $6045 = $1612 A's share. 3000 x 10=30,000. |, or of $6045 = $2015 B's share. 4000 x 9 = 36,000. f$, or f of $6045 = $2418 C's share. 90,000. 6 3 + 4+6= 13 parts. T \ of $195 = $45 share of first boy. & of $195= $60 " " second boy. A of $195 = $90 ' ' " third boy. 7 1000 + 1 500 + 1 800 + 2000 + 2700 = 9000 total indebtedness. or i $6000 = $666.66| A's share. , or i " =$1200 C's " , or | " = $1333.33 JD's " 8CO E's " 102 PARTNERSHIP 8 5175-7- 6210= 83 eta. 1320 x $.83^ = $1100. 9 180+250+400=830 tons. $f of 249 = 54 tons, A's loss. |f of " =75 " B's " " =120 " C's " 10 If A's = 1, then B's = 3, and C's = 2. Total 6 parts. iof $786 =$131 A's loss. | or J of $786= $393 B's loss. I or J of $786= $262 C's loss. C's share. i of $600=$300 A's gain. 300xl2=$3600 total capital 1 of $3600 =$1800 A's investment i "$3600 = $600 B's i "$3600= $1200 C's 12 3 x 20= 60 $1000 - $100= $900, am't to be divided 5 x 30= 150 #0 , or f of $900 = $257} + $100= $357}, share 210 of first. Jf$, or f of $900=$642f share of second. 13 5316 X .25= $1329, contract price. 5 x 45 x 4= $900 cost of teams. $1329 -$900 =$429 profit. $ of $429 = $171.60, share of first, f of $429 = $257. 40 share of second. 14 3 + 4+ 5 =12 parts. ^, or J of 1728=432 A, or Jof " =576 ^ z of " =720 15 1200 x $1.10= $1320 A's share. HI <> f $3090= $990 A's share 800x 1.25= 1000 B's " ffl" " =$750B's " 1600xl.l2J= 1800 C's " JH " " =$1350 C's " $4120 PERCENTAGE 103 PART III. PERCENTAGE 209 Page 182 1 $75-r- .03 = $2500 2 } of $1728= $432 3 J = $750, f = 5x$750=$3750 4 3200-7-6400=. 20= 20%. 5 ifa of $9900 = $66. 6 $75-7-^ = $4500. 7 25.92-=-db=$1728c 8 $102.50-7-20500= .00* = 9 | 'of $7288 = $4555. 10 I of $36 = $6. 11 490-J-5000 =.09| = 9|%. 12 $6.50= J, |=8 x $6.50= $52. 13 | of $1683.25 = $673.30. 14 $150 = , f = 3 X $150 = $450. 15 $729.80=, J = J of $729.80 = $364.90. | = 3 x $364.90= $1094.70. 16 2.50-7- 20=. 12J=12J%. 17 ,02 Jx $400 = $10. 18 .018 x $1500 =$27. 19 13.504-81=. I6f=16%. 20 $37.50 is 6%, l% = i of $37.50 = $6.25. 100% = 100 x $6. 25 = $625. 104 PRACTICAL WORK IN PERCENTAGE PRACTICAL WORK IN PERCENTAGE 212 Page 183 1 Tfoof $3300 =$99. 2 10%, or T V of $2500 =$250, for board; 5%, or $ of $2500= $125, for clothing; 18% or & of $2500 = $450, for incidentals. $120-r-f = $300. 5 2J-5-20 = &, = J, 6 125% = f. $6.25-rf=$5. 7 $36-:-. 90 = $40. 8 1260--8750Ffl4f%. 9 $2150-7- .05| = $40,000. 10 37% = f, | of $2400 = $900. 214 Page 185 1 $35 S. P. 100% C. 40% gain. $35 is 140% of 35-M.40=$25 2 100% C. 37J%G. 137*% S. P. 137 \% of $7.20= V of 7.25 = $9.90. 3 $35008. P. $500 loss. $3500 + $500 = $4000, 500 is what part of 4000 ? 500 ^ 4000 = \ = 4 100% C. - 16|% loss. = 83% S. P. $3.75 = 83^%, or f ; 3.75-H = $4.50. 5 $3840C.100%C.-2i%L. $3840 -$96 = $37448. P. . 3840 x .02 J = $96 lose. 6 $1 cost of 12 Ibs. $1.20 S. P. of 12 Ibs., .20 G. .20^-1 = . 20 = 20%. PRACTICAL WORK IN PERCENTAGE 105 7 .50 S. P. - .37 J C. = 12J G. .12i+.37 = .33 = .33 J%. 8 1.05 S.P. 100% C. -12J% L. = 87J%, or$S.P. 1.05-5- = $1.20. 9 100% = C. 125% = marked price. | of 125% = 100% = S. P. \ Sold at cost, $1.50. 10 | cost of part sold. selling price. J gain. 11 2240 Ibs.- 2000 lbs. = 240 Ibs. 243 Ibs. gamed on sale of 2000 Ibs. = 2-10-5-2000 = 12%. 12 $1 = | of cost. $l-=-f=$1.25C. $1.25x1.10=41.37! S. P 13 $7 = 14f%, or, ^ofcost. 7x$7 = $49cost. $49- $7 = $42 S. P 14 16cts.=$i, 20% = *. fof$| = 20cts. 15 300-7-12=25 doz. $1.50-5-25 = $.06. $.06xl41f% = 8J cts. 16 $3.50=14%. 3.50-^.14= $25 cost. 2.75+25 = . 11 = 11%. 17 ' lOc. = i of cost. 8 x 10 cts. = 80 cts. cost. 18 $160= f. $160-5-f = $180 C. of second and S. P. of first. $180-5- V = $162 C. of first. $162 - $160= $2 loss. 19 $840+12= $70 cost per A. 4 x $85= $340 S. P. of first. 3x$75 = $225 " " second f of $70=$60S.P. per A.of third. 5x$60 = $300 " "third. $865 total S. P. $865 S. P. - $840 C. = $25 gain. 25+840=2^%, 106 PRACTICAL WORK IN PERCENTAGE 20 $35 = | of C. of first and of cost of second. 35-7-1 = $30 C. of first. 35-r I = $42 cost of second. $30 + $42= $72 cost. $35 + $35 = $70 S.P. $72 - $70 = $2 loss. 2-r72=2|%. 21 f of 75c. = 90cts. f of 95cts. = $1.14. $ of $1.10 = $1.32. 22 55c. + 5c. = 60c. cost of each chair. $.60 x 120 = $72 total cost. $96 S. P. - $72 C. = $24 G. 24^-72=^=33^%. 23 \ leaked out. $.08-7- 1 = $.09 S. P., equivalent to cost. Gain ^, S. P. V of $.09 = 10 cts. * 24 7. 82-r. 92= $8.50 cost of f. $8.50-H = $21.25 cost of whole c'sk 108% of $21. 25 = $22.95. $22.95 -7.82= $15.13 S.P. of rem. |. 25 100% C. + 10% G. = 110% assumed S. P. 110% -95% = 15%. $5.55=15%, co?t=$5.55-r.l5 = $37. 26 $65 - 37.50= $27.50 cost of material. 110% of $37.50=41.25 cost of labor. $27.50 + $41.25 = $68.75 total cost. 120% of $68.75 = $82.50 S. P. 27 ljx$1.06 = $1.20 S. P. per cental. 240 x $1.20 = $288 S. P. 240 x .96= 230.40 C. 75% of 288 = $216 am't really received. $230.40 C.-$216 S. P. = $14.40 L. $14.40-7- $230.40 =6J% loss. 28 Cost 3 for $5 or $20 per dozen. $20 x 3= $60 C. + 10 G. = $70 S. P. $70 -f 36 = $1.94| av. S. P. $10-j-$60=l = 16f% gain. 29 $31.25=| of C. $31. 25 -rf = $37.500. $37.50-v- 25 = $1.500 per yard. 30 100 oranges - 5% loss =95 oranges. 95 x C. = $.63 S. P. $.63J S. P. - $.40 C. = 23^ cts. gain. 23S-f-40=58j%. LOSS AND GAIN 107 LOSS AND GAIN 216 Page 189 1 1500 X.07H 112.50 loss. $1500 -$112.50= 1387.50 S. P. 2 $500-r .02^ = 20,000 cost, + $500 =$20,500 S. P. 3 $1320-7- .99 = $1333 J- cost. $1333 J - $1320 = $13 loss. 4 75-:-2000=3|%. $2000 -$75 = $1925 S. P. 5 $1085 x 1.07f= $1170.25 S. P., - $1085 C. = $85.25 gain. 6 $3050 - $2375 = $675 gain -7- $2375 = 28 &% . 7 $147-7-. 07 = $2100 C., + $147 G. = $2247 S. P. 8 $2085 -H = $2502 C . , - $2085 = $417 loss. 9 $12.50- $10=2.50 loss,-r$12.50 = 20% loss. 10 $18.50-v-if = $19.73 J- cost, - $18.50 = $1.23J loss. 11 $45-7-.03J = $1350 C., + $45 = $1395 S. P. 12 $1300x1.30 = 1690 S. P., - $1300 = $390 gain. 13 $125x6= $7500. -$125 = $625 S. P. 14 $480-j- .73 J = 654.^ r C. - $480 = $174 T 6 r loss. 15 $920 x .85 = $782 S. P. $920 - $782= $138 loss. 16 $840-r.l3j = $6300 C., - $840 = $5460 S. P. 17 $95.50 -$5.50= $90 C. $5. 50 ^$90 = 6% G. 108 COMMISSION 18 $200-$175 = $25G.,-j-$175=14f%G. 19 $7000 x. 14= $980 G., + $7000 =$79808. P. 20 $25.50 X. 50 =$51 C., + $25.50= $76.50 S. P. 21 $175-$150=$25G.,-f-$150 = 16|%. 22 $15 x .80= $12 S. P. $15 - $12= $3 loss. 23 $15-5-. 83 = $180., -$15 = $3 loss. 24 $1030-rl.03 = $1000 cost. COMMISSION 218 Page 190 1 50x$14=$700S. P.,x.03 = $21 com. $700- $21 = $679 net. 2 $10.50+ $1.14 = $11.64. $11. 64 x 50= $582 C. $679 S. P. - $582 C. = $97 G. 97-j-582=16 %. 3 100x$5.50 = $550,xl.03 = $566.50 B. price 4 $3120-7-1.04 = $3000 cost. $3120- $3000 = $120 com. 5 $3120 x $1.20= $3744 S. P.,-=-750=$4.99 S. P. per bbl. 6 6k% of 32 cts. = 2 cts. com. 32 cts. - 2 cts. = $.30 cts. per doz. 7 $14000 +$2700 + $1300 = $18,0008. P., x.01| = $315 com. 8 $31500-M.05 = $30,000-MOO=300 bales. COMMISSION 109 9 $2490-5-1.031 = $2400,xli = $2805 S. P. $2400-5- $.08 =30,000 Ibs. $2905-5- $30,000 =$.09^8. P.perlb. 10 35% of $5 = $1.75. $1400-;- $1.75 = 800 vol. 11 $87.60-5-.03=$2920. 12 3000 x$li= $3500 S. P. $3500 x .02f =$80 com. $3500 -$80 =$3420 net. 13 $128.75-5-$5150=2J%. 14 $5115 -$165 = $4950 B. P. $165 -5- $4950 = 3 J%. 15 $123-5- .03 = $4100. 16 $275 + $1720 = $1995 cost. $25 x 12 =$300 rent., x. 05 = $15 com. ' $300- $15 = $285. $285 -5- $1995 = 14^%. 17 f of 5600 = $4200, x .06J = $262.50 com. $4200- $262.50 =$3937.50 proceeds. 18 $1890-5- .90 = $2100. 19 5% of $1.20 =$.06. $1.20+ $.06 + $01J = $1.271 C.,x 1.25= $1.59f S. P. 20 $2689. 75-3-1.01*= $2650. $2650-r-.03| = 79,500 Ibs. 21 $25-5- .03= $750. $750-5-. 08 J = 9000 ibs. $7754-9000 = $.08ft per Ib. 22 $5150-1-1. 03 =$5000. $5000 -r $5 = 1000 bbl. 110 COMMISSION 23 100x480=48,000 lbs.-MOO=480 cwt.,x$18=$8640, x.05 = $432 com. 24 450 x $13 = $5850, x. 05 = $292.50 com. $5850 -$292. 50 = $5557.50. $555 7. 50-7- 1.04 =$5343. 75 wool investment $5557.50 -$5343.75 = $213,75 com. $5343.75+- $-221 = 23,750 Ibs. $292.50 + $213. 75 = $506. 25 total com. 25 500 x $2.50= $1250+ $12= $1262. $1287- $1262 =$25 com $25 -i- $1250 =2%. 220 Page 193 1 $165-r$6600=2%rate, $6600 -$165 = $6435 proceeds. 2 $140+. 01| = $8000 C. 3 $5600^1.025 = $5463.41cost. $5600 - $5463. 41 = $136.59 com. 4 $13.50+- .01$ = $900 S. P. $900- $13.50 = $886.50 proceeds. 5 $8732 x .02 = $174.64 com. $8732 - $174.64 = $8557 .36 proceeds 6 $14.21 + $568.38 = 2J% rate. 7 $420+- $14,000 = 3% rate. 8 $2209 + $141 = $23508. P. $141-v-$2350 = 6% rate. 9 $4000 -$250 =$3750. $250 -7- $3750 =6|f% rate. 10 $2182.80-M.02= $21400. $2182.80 -$2140 = $42.80 com. 11 $4872 -$4800 =$72 com. $72 -H$4800 = l*% rate. 12 $48.29+-. 02| = $17568. P. INSURANCE 111 13 $1500-$41.12 = $1458.88. $41.124- $1458.88 = 2|%. 14 $4975 + $25= $5000 S. P. $25 v- $5000 = *%. 15 $74.25-r. 061 = $1188 cost. 16 $2000 x .00 J = $5 com. INSURANCE 222 Page 195. 1 $5500x .OOf = $44 premium. $5500- $44 =$5466 loss. 2 $110-r.02| = $4000 value. 3 360-^48,000 = . 0075 = f%. 4 $4000-i-2 = $2000, x .01 = $20 premium. $2000 - $20= $1980. 5 $62.50-:-. 025 = $2500. $2500= , f = I of $2500=$3750. 6 $3600 -$3528 = $72 com. $72-h$3600 = 2%. 7 $7600-^1.01| = $7500 insurance. $7600 - $7500 = $100 prem. 8 $6000 + $1800 + $1200 = $9000, x = sj COO ). $106 - $1 = $105, ^6000 = 1|%. 9 $6500 + $500 = $7000, x f - $5000. f % of $5000 = $37 .50. $7000 + $37.50= $7037.50 total cost. $7037.50 x .96 = $6756. 10 $2846.25-r 1.035 = $2749.951 am't invested,-:- $5^=500 bbl. U% of $2746.95 = $34.374 ins., + $2846.25 = $2880.624 total C. 10% of $2880.624=$288.0624gain + 2880.624cost = $3168.68 S. P.,-i-500 = $6.337 + . 112 TAXES 12 $1500xf% = $11.25x2 = $22.50 first cost. 43200 X |% = $28 2d cost. $28 - $22.50 = $5.50 favor of first. 13 3%x3 = 9%. 9% of 2400 = $216. $2400- $216 =$2184 loss. [Not strictly true, as company had use of premium at ruling interest rates, which lessens the loss considerably.] 14 1500 x|% = 12, x $4.86= $58.32. 15 $2562 -$42 =$2520. 42^2520=1%. 16 $19.80 x 8 = $158.40 annual payment, x 20= $3168. 17 [6f% should read $6fJ $6-7-.01J 18 $10.50-f- .0175 = $600~ = $900 cost. 19 $2100 x .008 = $16.80 premium + $2100 = $2116.80. 20 $6000 cost + $75 insurance + $900 repairs = $6975 total cost. $6975 + ( of $6975) = $9300 S. P. house. $9300-rl.03 = $9000-i-$4 = 2000 bbl. 2000 bbl. x $4= $8000 S. P. , - (3J% of $8000) = $7750 received. $7750- $6975 = $775 gain. 775^-6975= TAXES 225 Page 198 1 1200 x $1.50 = poll tax. $21800 -$1200 = $20, 000. 20,000 -f 4,000,000 = ,^= J%. 2 $4000 + $1800 = $5800 x J% = $29 property tax . $29 + $1.50 = $30.50. TAXES 113 3 $16- $1.50 =$14.50 property tax. $14.50-r-. 005 = $2900. 4 $5500 + $1700 = $7200 x .005 = $36 property tax. $36 + (3 x $1.50) = $40.50. 5 $4500 -r $1 ,000,000 = .0045 = 45 cts. on the hundred. 6 $8500 -$500 =$8000. $8000-r. 016 = $500,000. 7 $3000-r .003 = $1 ,000,000. T ^% = 3 mills on the dollar. 8 $3500x.00 = $7. 9 $4750^-. 95 = $5000 tax. $5000 x $450,000 =!%. 10 $7500 + $2750=$10,250. $10,250 x .008 = $82 property tax. $82 + (2 x $2 poll tax) = $86. 11 485 x $2= $970 poll tax - (10% of $970) = $873. 12 | of $2000 = $1500 x .008 = $12 insurance. f of 2400 = $1600x .014=$22.40 tax. 20% of $2400 = $480. $480 + $12 +$22.40 =$514.40-1- 12 =$42.86f per month. 13 $2850-r .95 = $3000. tax. $30004- .005 = $600, 000. 14 $77.50 x 12 = $930 yearly rent. f of 7000 = $5000 x .0075 = $37.50 insurance. | of $7000 = $5250 x .01 = $52.50 taxes. $37.50 + $52.50 =$90 total expenses. $930 - $90- $840 true income. 840-7-7000= 12%. 114 DUTIES DUTIES 227 Page 200 1 100 x $.25 =$25 on oranges. 60x$.30=$18 on lemons. $25 + $18 = $43 duty. 2 100 x $15 = $1500 x. 25 = $375. 3 11 x 2240 Ib. = 24640 lb., x .009 = $221.76 4 12 x 225 lb. = 3060 lb. x $.80= $2448 original cost. 3060 lb. x $.35 = $1071 duty. $2448 x .35 = $856.80 ad val. $2448 cost +$1071 duty +$856.80 ad val. + $72.50 charges: $4448.30 total cost. 5 80 x$7. = $560 champagne 90 x 2. = 180 brandy 94 x .50= 47.25 wine 75 x .35= 26. 25 ale ~$8T3~J50 total 6 $2283. 60-J-. 60 =$3806. 7 1280 yd. x $.30 = $384 duty on carpet. 1440 " x .20= 288 duty on tapestry. $725 " x .30= 217.50 ad. val. on carpet. $650 " x .30= 195 ad. val. on tapestry. $1084.50 Total. 8 840lb.-7-56lb.x$.20 = $3. 9 1000 T.x $.75 = $750. 10 2)0 T.x 20 x. 08 = $320. STOCKS 115 11 50xl081b. = 54001b.x$.01 = $54. 12 $94 x. 20 =$18.80. 13 200 X $.45 = $90 x $.20 = $18. STOCKS 228 Page 202 2 $1000 x .OOJ = $2.50 brokerage + $1020 = $1022.50. 3 $1000 x .04 = $40 dividend. $40 4- $1022.50 = 3f %. 4 $3204-. 04 = $8000 of stock=80 shares. $102x80 =$8160. 5 $720^- .09 = $8000 of stock = 80 shares. 80 x $60 = $4800. 6 .074-1.4525 = 4ff%. 7 .124-1.6925 = 7*V 7 % B. of Cal. .094-1.25 = 7$ F. N. 8 $99-$82 = $l7i. $28604- $17| = 160 shares. 160 x $82 =$13, 120. 10 $4000 x .00| x $25 taxes. $275 - $25 = $250 income. 250-v- 5000=5% house. $5000x1. 12 = $5600. $5600 -7- .70 =$8000 of stock. $8000 x .03| = $280 income. 280.4-5600 = 5% stock. 11 $14684- $91. 75 = 16 shares. 12 150x$2.50=$375. $375 x. 00 J= 1.87* com. $375 + $187i= $376.87 J. 116 INTEREST 13 .99x.lH=ll%. 14 50 x $2.50 = $125. 100x$H = $125. $250 X. 00 J = $1.25 com. $250 + $1.25 = $251. 25. 15 109J- $101 = $8.501ossoneachshare. $340-r$8.50 = 16 $570-i- $6 =95 shares. 95 x $66.50 =$6317.50. 17 .054-.87|=5|ff% S. P. R. R. .06-=-.99 = 6&% O. N. 18 24 x $53.50 = $1234. $1284-i-$107 = 12 shares. 19 $1182.50-J-$118 = 10 shares. INTEREST 231 Page 207 Time yr. mo. da. Interest on $1. Interest on Principal > Amount 1 1 1 8 $.006J $ 11.9068 $ 191.41 2 2 11 6 .176 57.20 382.20 3 3 2 16 .192| 146.1858 904.94 4 2 3 22 .138s 142.0293 1166.28 5 2 14 .012| 7.2088 591.71 6 1 '3 11 .076| 55.7687 781.61 7 3 6 24 .214 83.0213 470.97 8 24 .004 .1688 42.37 INTEREST 232 Page 207 117 Time yr. mo. da. Interest on$l. Interest on Prin. 1 030 OH .Olf .02 $ 6.00 7.50 9.00 2 230 :UI .18 43.53| 60.95J 69.66 3 2 .08 57.46 4 3 3 .10 22tf 94.071 5 3 20 .ISA 109.694 6 2 2 25 .166H 59.48 7 2 5 17 .049& 83.772 8 2 14 .012 11.229 9 4 21 .019& 14.648 10 5 24 .019* 16.916 11 109 .071f 180.236 12 6 .04 154. PROBLEMS IN INTEREST 238 Page 212 1 $360 X .06 =$21. 60 int. for 1 year. $97.20-r $21.60 4 years 6 months. yr. 118 PROBLEMS IN INTEREST 2 $900 x .07 = $63 int. for 1 yr. $84-r-$63 = lJ yr. = l yr. 4 mo. $900x.08=$72 " " $84-5-$72=l| yr. = lyr. 2mo. 3 $1 @ 5% for 2 yr. 6 mo. = $.125 int. $62.50-7-$.125=$500. 4 $145 @ 1% for i yr. = $.725 int. $5.80-f-$.725 = 8; or 8% 5 $240@1% for given time = $8.40 int. $56-7-$8.40= 6; or 6%. 6 $1 @7% " " = $1.23amt. $296-5- $1. 23 J= $240. 7 $1@6% " " =$1.03 " $700-5-11.03= $679.61 8 $720 @ l\% for one month = $10.80 int. $16.20-5-$10. 80= 1J mo. = l mo. 15 da. 9 $l@i% per mo. for given time = $1.02 amt. $400-7- $1.02 = $392. 16. 10 $1 @ 6% for given time = $1.03 amt. $390-7- $1.03 =$378.64 P. W. $390 -378.64= $11.36 disc. 11 $1 @ 8% for given time = $1.04 amt. $104-5-$!. 04 = $100 P. W. .'. Nodiff. 12 $700 X. 08 =$56 int. $450x .08 = $3(> int. 1 yr. $56-r$36=l yr. 6 mo. 20 da. 13 $250x1. 04 =$240.38 P. W. $250-5-1.06= 235.85 P. W. $250-7-1.09= 229.36 P. W. $705.59 total P. W. 14 $7500-=- 1.02 = $7352.94 P. W. ; or cost. $7500 S. P. - $7352.94= $147. C6 gain. PROBLEMS IN INTEREST 119 15 $35 x 12 = $420 annual income. $420-h$3400= 12 T V %. 16 $275 @ 1% for given time =$9.35 int. $56.10-f- 9. 35 = 6; or 6%. 17 $1 @ 7% for given time= .240$ int. $103.95-J-$.240525 = $432 prin. 18 $1 @ 6% for given time = .005 int. $100-j- .005 = $20,000 prin. 19 $1 @ 6% for given time = 1.2185 amt. $926.06 -r $1.2185 = $7 60 prin. 20 (Same as example 8.) 21 $125 x .04= $5 int. 1 yr. $16.50-v-$5=3 yr. 3 mo. 18 da. 22 $760 @ 1% for given time = $27.67f int. $166.06-5-27.67 = 6;or6%. 23 $1 @ 6% for 2 mo. 9 da. = $1.0115 amt, $221.27+$1.0115 = 24 $1 for given time @ 8% = .02 int. $125-f- .02 = $6250. 25 $1 for given time @ 6% = $1.1575 am't. $560.23-;- $1.1575 = $484. 26 $90 x .07 = $6.30 int. 1 yr. $10 -f $6.30=1 yr. 7 mo. 2 da. Jan. 3, 1882. 27 $460 x .05 = $23 int. 1 yr. $71.30-v-$23=3 yr. 1 mo. 6 da. 28 $200-f-1.01 =$198.01. 300^-1.015= 295.56. 400H-1.02 = 392.15. $885.72 total P. W. 120 PARTIAL PAYMENTS 29 $210-i- 1.04 =$201. 92 P. W. ; or S. P. $201. 92- $200 = $!. 92 G. 30 $410@1% for given time = $4.51 int. $27.064- $4.51 = 6; or6%. 31 $210-r$.28 (int. on $1) = $750 prin. 32 $550 x .06= $33 int. 1 yr. $102-r$33=3 yr. 1 mo. 3 da. 33 $270 x. 06 = $16.20 interest. $270-7-1.06 = $254.717 P. W. $270 - $254.717 = $15.283 discount. $16.20 interest - $15.283 discount =$.917 difference. , 34 7 \% - 6% = \\% gain per year. $35.10-7- .045 = $780 principal. 35 $75@l%for4mo. = $.25int. $2.00-1- $.25 = 8; or 8%. 36 $1000-7-1.01 = $990.09 P. W. 500-7-1.025= 487.80 P. W. 500-M.015= 492.61 P. W. $1970.50 total P. W. PARTIAL PAYMENTS 240 Page 215 1 $1500 prin. 54 int. 1554 amt. 500 pymt. 1054 new prin. 21.08 ^nt. 2 $480 prin. 16.80 int. 496.80 amt. 196.80 pymt. "300 N. prin. 10.50 int. 1075.08 amt. 500 2d pymt. 310.50 amt, 214 2nd pymt. 575.08 new prin. 2.30 int. $577.38 balance due. 96.50 N. prin. 3.37 int. $99.87 bal. due PARTIAL PAYMENTS 121 $1000 prm. 50 int. 1050 amt. 50 pymt. 1000 N. prm. 26.60 int. 1026.60 amt. 450 2nd pymt. $ 576.60 bal. due $1230 prin. 11.265 int. 2m. (.009$) 1241.275 amt. 98 1st pymt. 1143.275 N. prin. 16.768 int.3m6d(.014f) 1160.043 amt. 500 2nd pymt. 660.043 N. prin. 10.386 I. 3ml3d(015H) 670.429 amt. 290 3rd pymt. 380.429 N. prin. 4.649 1.2m20d(.012f) 385.078 amt. 100 4th pymt. 285.078 N. prin. .914I.21da.(.003iV) $285.992 balance due. 5 $800 prin. 35.333 1. 5m. 9d(.044) 835.333 amt. 200 1st pymt. 635.333 N. prin. 3.7061. 21da.(.005f) 639.039 amt. 50 2d pymt. 589.039 N. prin. 19.62 I. 4 mo. (.033J) 608.659 15. 3d pymt. 593.659 N. prin. 9.8941. 2 mo. (.0161) $603.553 balance due. 6 $365 prin. 3.65 I. 2 mo. (.01) 368.65 amt. 68.65 1st pymt. 300 N. prin. 3.40 I. 2m. 8d. (.011J) 303.40 amt. 103.40 2d pymt. $200 balance due, 122 PABTIAL PAYMENTS $2500 prin. 70.972 int. 2570.972 amt. 500 1st pymt. 2070.972 N. prin. 27.89 int. 2098.862 amt. 750 2d pymt. 1348.862 new prin. 38.02 int. $1386.882 balance due. $500 prin. 3.33Jint. 1 mo. (.00$) $503.33 amt. 100 1st pymt. 403.33 N. prin. 2.69 int. 1 mo.(.00) 406.02 amt. 100 2d pymt. 306.02 N. prin. 2.04 int. 1 mo. (.OOf) 308.06 amt. 100 3d pymt. 208.06 N. prin. 1.378 int. 1 mo.(.OOf) $209.447 balance due. 8 $960 prin. 13.20I.2m.6d.(.013|) 18.00 I. 3 mo. (.018|) 991.20 amt. 370 1st and 2d pymts 621.20 N. prin. 3. 8825 I.I mo. (.006}) 625.08 amt. 300 3d pym $325.08 balance due. 10 $1200 prin. 17I.2m.25d.(.014|) 1217 amt. 500 let pymt. . 717 N. prin. 9.6795l.2m21d(.013i) 726.68 amt 500 2d pymt. 226.68 N. prin. 2.266 int. 2 mo. (.01) $228,946 balance due. COMPOUND INTEREST COMPOUND INTEREST 242 Page 217 123 1 $1000 prin. 1.06 x 3 $425 1.01 429.25 amt. 3 mo. 1.01 433.542 amt. 6 mo. 1.01 1060 amt. 1 yr. 1.06 1123.60 amt. 2 yrs. 1.06 1191.016 amt. 3 yrs. 1.06 437.87 amt. 9 mo. LOOf 3262.4769 amt. 4 yrs. 1000 440.789 amt. 11 mo. \ 425 $15.80 comp. int. 4 $250 1.02* 256.25 amt. 6 mo. 1.02* 262.66 amt. 1 yr. 1.00 T 5 a 262.48 comp. int. 2 $300 1.04 312 amt. 6 mo. 1.04 324.48 amt. 1 yr. 1.04 337.46 amt. 1 yr. 6 mo. 1.001 339.709 amt. 1 yr. 7 mo. 300 $39.709 comp. int. 263.75 amt. 1 yr. 1 mo. 250 13.75 comp. int. 124 COMPOUND INTEREST 5 $500 1.06 530 amt. 1 yr. 1.06 361.81 amt. 2 yrs. Utt| 570.227 amt. 2yr. 3 mo. 500 $70.23 comp. int. 6 $490 1.02 499.80 amt. 3 mo. 1.02 509.796 amt. 6 mo. 516.60 amt. 8 mo. 490 $26.60 comp. int. 7 $1500 1.03J 1552.50 amt. 6 mo. 1573.33 amt. 8 mo. 9 da. 1500 $73.33 comp. int. 8 $275 1.01J 279.125 amt. 3 mo. 1.01* * 283.31 amt. 6 mo. l.OH 287.559 amt. 9 mo. 275. $12.56 comp. int. 9 $800 1.06 848 amt. 1 yr. 1.06 898.88 amt. 2 yr. 1.02 916.857 amt. 2J yr. 800 $116.86 comp. int. 10 $1200 1.03 1236 amt. 6 mo. 1.03 1273^08 amt. 1 yr. 1.03 131 1.27 amt. lyr.6mo. 1.001 1312.58 A.I y. 6 mo. 6 d. 1200 $112.58 comp. in DISCOUNT 125 D ISCOUNT 243 Page 218 1 Discounted 2 mo. $700 x .01= $9.33 discount. $700 - $9.33i = $690.67 proceeds. 2 Discounted 32 da. $850 x .01 r V = $9.06f discount. $850 - $9.06 = $840.93 proceeds. 3 $1400 x 1.04 =$1456 amt. of note. Discounted 3 mo. $1 456 x .02 = $29.12 dis. $1456- $29.12 = $1426.88 proceeds. 4 $900 x 1.03 =$927 amt. of note. $927 x .02 = $18.54 discount. $927 - $18.54 =$908.46 proceeds. 5 $250 x .01 = $2.50 discount. $250 - $2.50 = $247 .50 proceeds. 6 Discounted 23 da. $1850 x .OOf $ = $14. 18 discount $1850 - $14.18= $1835.82 proceeds. 7 $525 x 1.02 = $535. 50 amount of note. Discounted 3 months. $535.50 x .03 = $16.065 discount. $535.50 - $16.065 = $519.435. 8 $300x1. 04 = $313. 50 amt. of note. Discounted 3 mos. $313.50 x .05 = $15.675 discount. $313.50 - $15.675 = $297.83. 9 $1140 x 1.08= $1231.20 amt. of note. Discounted 10-& mos. $1231.20 x .07 &= $89.467 discount. $1231.20-$89.467 = $1141.73 proceeds. 10 Discounted 2 T 2 ^ mos. $1375 x .Olf = $24.44 discount $1375 - $24. 44 =$1350.56 proceeds. 11 $735x1. 025 = $753.375 amt. of note. Discounted 48 days. $753.375 x .032= $24.108 dis. $753.375 = $24. 108 =$729.267. 126 COMMERCIAL DISCOUNT, AND EXCHANGE COMMERCIAL DISCOUNT 244 Page 220 1 $450x.60=$270x.95 = $256.50ans. 2 .75x.95=.71i. $1.00 -.71i = .28f; or, 28% discount. 3 $250 x. 65 = $162.50, at 35% dis. $250 x .30 = $175 x. 95 = $166.25, at 30 and 5 dis. $166.25 - $162.50=$3.75 more. 4 $810^.90 = $900-r.90=$1000ans. 5 $200 x. 95 = $190. 6 $830 x .70= $581 x .90= $522.90 x .95 = $496.75 cost. $496. 75x1. 20 =$596. 10 S. P. 7 $76-r- .95= $80 invoice price. 8 $425.50 x .90 =$382.95 x .95 = $363.80 cash value. 9 $725 x .97 = $703.25 cash value. 10 $5.50 x .90= $4.95 x .90= $4.45 price paid. 11 $1.504- .83= $1.80^. 75 = $2.40 list price. 12 $700x.85 = $595x.96=$571.20amt. received. EXCHANGE 245 Page 230 1 $5000x1. 015 = $5075 cost of sight draft. $5075 x.98= $5008.33$. AVERAGE OF PAYMENTS 127 2 $580 x. 99 = $577.10. 3 2481.25 -7- .99i = $2500. 4 320 x $4.95 = $1584 cost of sight draft. $1584 x .98| = $1565.52. 5 $1566.15-r-. 985 = $1589.94. 6 $1 + .015 premium - .015 int. allowance = $l/.cost= $4500, 7 4000 x. 186 = $744 x. 99 = $736.56. 8 $800 - $794 = $6 discount. 6-r800= f %. 9 $765 x 1 .00| = $770.7375 cost of sight draft. $770.7375 x. 99 J = $769.04. 10 $799.60-7-. 9945 = $804.022 cost of $800 sight draft. $4.022 premium -r $800 = J + % . 11 1000 x .186= $186. $1 + .015 premium - .015 int. allowance = $1.-. Cost=$186. 12 $162.75 = 875 fr. $1 + .015 premium- .015 int. allowance = $1 /. Draft =875 fr. 13 26 fr. pr. = less than $.186 to fr., hence exchange is at a discount. 500 x 26 fr. = 13,000 fr. x .99 = 12,891f fr. AVERAGE OF PAYMENTS 248 Page 233 1 $180x5= 900 mo. 250x8=2000 100 x 9 = 900 It equals the use of $1 for 3800 mo $530 3800 mo. 3800-r- $530 = 7 mo. 5 da. 128 AVERAGE OF PAYMENTS 2 $ 800x3 = 2 00 mo. 6400 mo. -i- 1800=3 mo. 17 da. 1000x4=4000 $1800 6400 mo. 3 $150x3= 450 mo. 175x4= 700 200x6=1200 2350-7-525 = 4 mo. 14 da. $525 2350 mo. Apr. 8 + 4 mo. 14 da. = Aug. 22. 4 $390x16 =6240 da. 15,740-7-865= 18 da. 475x20=9500 $865 15,740 da. 5 $100x1 = 100 da. 150x18=2700 200 x 38 = 7600 10,400-5-450= 23 da. $450 10,400 da. May 31 + 23 da. = June 23. 6 $250x8 = 2000-7-400 = 5 mo. Ans. 7 550x6=3300-rlO=$330. 8 $1000x10 =10,000 mo. $250 x 4 = 1000 mo. 10,000 mo. - 5000 mo. = 5000 mo. 500 x 8 = 4000. 5000-r $250 (balance due) = 20 mo. Ana. $750 5000 mo. 9 $400x2=800mo. 1940 mo. -7- 705 = 2 mo. 23 da. 80x3=240. 225 x 4= 900. Mar. 22 + 2 mo. 23 da. = June 14. $705 1940 mo. AVERAGE 129 1 2 x $2.50 =$5 00 3x 3.00= 9.00 10 x 3.25 = 32.50 15 are w'th $46.50 2 10 X$ .90= $9:00 8x .95= 7.60 7x 1.00= 7.00 25 are w'th $23.60 AVERAGE 249 Page 235 $46. 50x15 = $3. 10 each. $23.60- 25 = $.94f per cen. 3 45x$.08 =$3.60$6.75xl.lO = $7.425S.P. 30x = 3.15 75 Ib. cost $6.75 8x$ .40 = $3.20 lOx .50= 5.00 18 cost $8.20 . Ib. 18x$.50=$9.00S.P.-8.20C. = $.80G. $.80G.-J-$8.20C. = 9fi%. $.80-5- 18=$.04$ per roll. 5 50gal.x$ .35 = $17.50 50 x .42= 21.00 5 x .40= 20.00 50 x .00 200 gal. are worth $58.50 6 121b.x$ .06=$ .72 9 x .08= .72 15 x .11= 1.65 17 x .13= 2.21 $58.50-7- 200= $.29|- per gal. $5.30-r53 = $.10perlb. 53 Ib. are worth $5.30 130 AVERAGE 51b.x$ .40 =$2.00 7 x .25= 1.75 10 x .20= 2.00 2 x .50= 1.00 24 Ib. cost $6.75 24 x $.30= $7.20 selling price. -$6.75 0. = $.45 250 Page 236 Answers variable, one solution given) 1 65 55 70 60 5 10 + 5 5 5 15 5 Hence 5 Ibs. of 55 ct. 15 Ibs. of 70 ct. 5 Ibs. of 65 ct. Or any mixture in the ratio of 1 Ib. of 55 ct.l Ib. of 60 ct., and 3 Ib. of 70 ct. 2 Three times the quantity of each obser ving the ratio 1, 1, 3. 3 1 $1.50 $1.00 1 $0 100 50 100 of wine to 50 water; or,the ratio 2, 1 If 30 gal. wine be used, it would take 15 gal . of water 4 20 gal. x $.64 = 1280. $2260^-34 = $.66 r Vpergal. 14 x .70 = 980. 34 52 35 40 50 56 66 r 8 7 $2260. 4 4 i*A 17+12 2 4 4 1*A 29 o These proportions multi- plied by 17 give 34 gal. of the 64 and 70 ct. mixtures and fulfill all the conditions of the problem/. One ans. will be 68 gal of 35 ct., 68 gal. of 40 ct., 246 gal. of 50 ct., and 493 gal. of 56 ct. PART IV POWERS, ROOTS AND MENSURATION Square Root 253 Page 240 1 10'24(32 5 3200 sq. rd. x 2 = 1600 9 sq. rd. 62) 124 124 16'00(40 rd. breadth. 16 2 80 rd. length. 2 33'64(58 25 6 40'96(64 rd. 108)T64 864 36 124) 496 496 3 640 A, = 102,400 sq. rd. 7 12 rds. sq. = 144 sq. rds. 10'24'00(320 rd. 9 4 144 sq. rds. - 12 sq. rds. = 132sq. rds. 62)124 1280 rds. Ans 12. (3.46 rd. len'thofC. 124 9 00 64)300 256 686) 4400 4 06ftxl48Jft=9801sqft. 4116 184 98'01(99 ft. 12 rdfl.- 3.46 rds. = 8.54. 189)1701 [Example should read : What is the difference in the 1701 length of their sides?] (131) J32 SQUARE ROOT 8 Metric. 23x2.47 A.x 1 60 = 9089.60 sq.rds. 90'89/60(95. 185) 989 381.32 rd. A. 925 1903) 6460 5709 19063) 75100 57189 8 4xl60sq.rd. = 640sq.rd 6'40.(25.29 + rd. 4 4 45)240 101.16 + rd. Ans. 225 502) 1500 1004 5049) 49600 45441 9 10xl60=16'00 16'00rd.(40rd. 16 4 00 160rd.offen. 1600 sq. rd. -7-4 = 400 eq. rd. 4'OOsq. rd.(20rd. "00 2Bidee20rds.= 40rds. 2 8. 4x20rds. = 160 200 rds. $2.25 x (200-160) = $90 in A's favor. 9 Metric. 2x (387.5 m.-f 174.8m.) = 1124.6 m. 387.5 m. x 174.8 m.= 67735 sq. m. 6'77'35Bq. m. (260.2m. S. 46)277 1040.8 n 276 dist. around sq. 5002)~~13500 10404 (1124.6m.- 1040.8 m.)x 1.25 fr. = 104.75 fr. 10 72 rd. x 98 rd. = 7056 sq. rd. 70'56 (84 1647656 656 (72 rd. + 98) x 2 rd. = 340 rd. 4x84rd. = 336rd. 340 rd. : 336 rd. : : $425 : ($420.) 11 128 in. x 32 in. = 4096 sq. in. 40'96(64 124JT96 496 CUBE ROOT CU BE ROOT 256 Page 245. 133 1 261(21 5 2744 (14 in. edge 8 1 1200 1261 300" 1744 61 120 1 16 1261 1261 436 1744 14 2 = 196sq. in.x6 = 2 1000 gal. x 231 =231,000 1176 sq. in. cubic inches. 6 Jof 4 s =32. 32(3.17+ ft. 27 231'000(61.3 + 2700 "5000 216 90 10800 15000 L 180 10981 279T 2791 1 288300 220900 6510 10981 4019000 49 1116300 lft'^0 294859 2064013 -LOGVF 9 1118139 3354417 7 1 s : 2 3 ::1728cu. in. : (13284 664583 cubic inches. 8 4238 kilos. = 4238 cu. dm . , 3 V576 = 24i n. = 2ft. onaS. 4- 1000= 4.238 cu.m. 2 3 = 8cu. ft. 4/238 cu. m. (1.6+ m. 1 300-3238 4 3750 sq. in. 4-6 = 625 area 180 36 of one face. V625 = 25E. 516 3096 25 s = 15625 cu. in. 4- 231 = % 67.64 gal. * 9 225 m. x 14.2 m. X .025 m. = 7Q 7?; rnVir m 134 TRIANGLES TRIANGLES 257 Page 248 10 2 + 10 2 =2'00(14.14 24)100 96 281)400 281 2824)11900 11296 2 20 2 -15 2 = 175(13.228 23)75 262)600 500 2642)7600 5284 26448)231600 217584 3 25 a -18 2 =3'01(17.349 1 27)201 189 343)1200 1029 3464)17100 13856 34689)324400 312201 4 40 2 +30'=25'00(50 25_ 00 5 8 2 + 3*=73(8.64 64_ 165)900 825 1704)7500 6816 '=5'20(22.8 4 42)120 84 448)3600 3584 7 22.8 + 2 =520-9 2 =4'39 39(20.95 409)3900 3681 4185)21900 20925 8 60 a +24 2 = 4176(64.62 88 124)576 496 1286)8000 7716 12922)28400 25844 9 250 2 -65 2 -5'8275(241.4 4_ 44)182 176 481)675 481 4824)19400 19296 TRIANGLES 135 LO 14 2 + 14 2 =3'92(19.79 1 29)292 J.3 1 U A. X 16U = 10UU 16'00(40 rd. on side 16 261 00 387)3100 2709 40 2 +40 2 =32'00(56.568 949)39100 35541 25 106)700 636 (19.79 + 14 = 33.79. 1125)6400 5625 11306)77500 67836 113128)966400 905024 11 40 2 + 30 2 + 12 2 =2644 26'44(51.419 25 14 Ans. = length of side. 101)144 40rd.-j-2=20 rd. 101 1024)4300 4096 15 ^"729= 9 length of side. 10281)20400 92+92+92-243 10281 102829)1011900 243(15.588 925381 25)143 125 305)1800 1525 3108)27500 24864 12 82 2 -36 2 =54'28(73.67 49 31168)263600 249344 143)528 429 1466)9900 8796 16 15 2 ^2= 112.50 112/50(10.6+ rd. side 14727)110400 206)1250 103089 1236 73.67 + 10 =83. 67 ft (10.6+)*= 112.50 rd. 136 SURFACES 17 28 3 -18 2 = 60(21. 44 41)60 *L 424)1900 1696 4284)20400 16836 28 a -15 2 =5'59(23.64 4_ 43)159 129 466(3000 2796 4724)20400 18896 23. 64 ft. + 21. 44 ft.= 45.08 ft. Ans. 18 58 2 + 72'=85'48(92.45 91 182)448 364 1844)8400 7376 18445)102400 92225 k !9 2Jft. = 30 in. 1 ft. = 18 in. 30 2 +18 2 + 12 2 =1368 13'68(36.98 in. 9_ 66)468 396 ' 729)7200 6561 7388)63900 59104 36. 98 in. = 3 ft. .98 in. 20 Height to eaves 20 ft. 30ft. -20 ft. = 10 feet height of roof from eaves 18 2 + 10 2 =24(20.59 405)2400 2025 4109)37500 36981 SURFACES 258 Page 250 1 20 rd. x 18 rd. -7-2 = 180 sq. rd. 2 (25 rd. + 35 rd.)-r-2= 30 rd. 30 rd. x 13 rd. = 390 sq. rd. 3 11 rd.x 2x3.1416= 69.1152 rd. IP x 3. 1416 =380. 1336 SUBFACES 137 4 (13 ft. X 10 ft.)-j-2 = 65 sq. ft. 65 sq. ft, -j- 3. 1416 = 20. 690412= radius 2 . V20.690412 = 4.548 ft. 5 40 a x 3.1416=5026.56 sq.ft.-r (9 x30) = 18.46+ sq. rd. 6 3 2 x. 7854=70.686 sq. ft. 7 6 ft. X5.196 ft.-r 2 = 15.588. Area of one triangle, x 6=93.528 sq. ft.,-j-9 = 10.4sq. yd. 8 135 sq. rd. x 2 = 270 sq. rds. or area of fall rectangle, -f- 18 rd. = 15. rd. side. 9 72 2 = 5184-J-2 = 2592 sq. ft. = square of 1 side = area of square. J of 2592 sq. ft. = 1296 sq. ft. Area of triangle. 10 256 sq. ft.-r(J of 12 ft.) = 42f ft. = 42 ft. 8 in. 11 (12in. + 6in.)-r-2 = 9in. aver. 18 ft. x f ft. = 13* sq. ft. 12 12ft. 6 in. = 150 in. 150 in. -f- 3. 141 6 = 47. 746 in. 13 VI : V9 : : 10 :( ); or, 1 : 3 : : 10 :(30) ; VI :V4 : : 10 : (20). 14 20 2 - 5 2 = 375 ft. (square of radius) . 375 ft. x 3.1416 = 1178.10 sq. ft. 20 2 x3.1416=1256.64 sq. ft. 1256.64 sq. ft. - 1178.10 sq. ft. = 78.54 sq. ft. 15 1 A. = 160 sq. rd.,-r. 7854 =203. 7108 (sq. of diam.). V203.7108 = 14.27+ rd.diam. 14.27 rd. x 3.1416 x$2 = $89.C6+ 16 (54 rd. x 72 rd.)-j-2 = 1944 sq. rd.,-+160= 12& A. ; 138 SOLIDS 17 (108rd. + 144rd.)4-2 = 126rd. arer. 126 rd. x96 rd.-r!60=75f A., x $85 = $6426 cost of land. (108 + 144+195.34) rds.=447.34 rd.,x$1.75 = $782.84| cost of fence. $6426 + 782.845 = $7208.845. 18 (12ft. + 8ft.) x 2 ft. X 2 = 80 sq.ft. 2ft.x2ft.x4=16sq. ft. corners. 80 sq. ft. + 16 sq. ft. = 96 sq. ft. 19 4 ft. x 3.1416= 12.5664 ft. circum. 5280ft.-M2.5664ft.=420+ 20 31.5 A. x 160=5040 sq. rd. (also sq. of one side.) 5040 + 5040= 10,080. V10080 = 100.399 rd. diagonal. 5040 sq. rd.-s-. 7854= 6417. 11 sq. rd. (sq. of diameter.) v'6417.11 = 80.10rd.diam.80.10rd.x3.1416=251.6rd.circum. SOLIDS 259 Page 254 1 4x3x2=24 cu. ft. 2 4 ft. X 3 ft. x 2 = 24 sq.ft. S. 4 ft. x 2 ft. x 2 = 16 sq.ft. top and bot. 3 ft. x 2 ft. x 2 = 12 sq. ft. ends. (24+ 16+12) sq. ft. = 52 sq.ft. 3 5in.x3.1416-j-12=1.309ft.cir. 1.309ft. x2 ft. = 3.27 \sq. ft. 4 6 in. x 3.1416= 18.8496 in. cir. x 8 in. = 150.7968 sq. in. side. 6 a x .7854=28.2744 sq. in. area of bottom. 150.7968 sq. in. + 28.2744 sq. in. = 179.0712 sq. in. 5 Area of base 28,2744 sq. in. x 8 in. = 226. 1952 cu. in. -r- 231 = . 979 gal. = 3. 91 qt. SOLID* 139 6 12 2 x .7854 = 113.0976 sq. in. , 8 2 x .7854=50.2656 sq. in. area of bases. 113.0976x50.2656=5683.90. V5683.90=75.38. 113.0976 + 50.2656+75.38=238.74x10x^=795.8+ cu. in. 7 (12 in. + 8 in.) 4- 2x3.1416 = 31. 416 in. av. circum. 31.416 in. x 10 in. = 314.16 sq. in. Area of bottom 50.265 sq. in. + 314.16 sq. in. = 364.885 sq. in., -T- 144 = 2.53 sq.ft. 8 1 qt. = 57 cu. in. 3 2 X .7854=7.0686 sq. in. area of bottom. 571 + 7.0686=8.17 in. 9 12 2 x 3.1416=452.3904 sq. in. = 3.1416 sq. ft. 10 1'x. 7854x1 in. = .7854cu. in. 57| cu. in. -+.7854 =73*. 11 12* x .7854= 113.0976 sq. ft. (area of base). 113.0976 sq. ft.x6 ft. x = 226.952 sq. ft. 226.952 cu. ft. x 128=1 cd. 98.952 cu. ft. 12 12^ x .07958= 11.45952 area of base 11.45952 sq. ft. x 2x^=7. 63968 cu. ft. 7.63968 cu. ft. X 1728 = 13201.426 cu. in., +-2150.4 = 6. 14 +bu. 13 12+-3.1416 = 3.82 ft. diam.,-7-2=1.9l ft. radius. 1.9P + 2 2 = 7.6481. V7.6481 = 2.765 slant height. 12 (cir.) x 2.765(slant H.) x = 16.59 sq. ft. = 1.844+yd. 14 20 x 231 cu. in. = 4620 cu. in. 18 2 x .7854=254.4696 area of base. 4620 cu. in. -7- 254.4696 sq. in. = 18.16 in. depth. ur i H IVERSITY 140 SOLIDS 15 254.4696 sq. in. (area of base) x 4 in. x = 339.2928 cu. in., -r 231 = 1.47 gal. 16 4 x .5236=33.5104 cu. in.,-i-57f = .58 qt. 17 5x231 cu. in. = 1155 cu. in. 1155-j-10 2 = 11.55 in. depth. 18 (12 + 16) x 10 x 2 = 560 sq.ft.area of sides, 16 ft, x 12 ft. = 192 sq. ft. floor. 192 sq. ft. -=-.07958 = 2412. 6665 circum. 2 V2412.6665 = 49.119 ft. circum., x 10=491.19 + ft. wall. 560 sq. ft. - 491.19+sq. ft. = 68.80 sq. ft. 19 60 ft. x 40 ft. x 20 ft. = 48,000 cu. ft. 60 ft. x 40 ft. x 8 ft. x = 6400 cu. ft. 48,000 cu. ft. + 6400 cu. ft. = 54,400 cu. ft. 20 14 2 x. 7854 =153. 936 cu. in. 153.936-7-144x20=21.38 cu. ft. 21 8000* mi. x 3.1416=201,062,400 sq. mi. surface. 201,062,400 sq. mi. x 8000 mi. x | = 268,083,200,000 cu.in. vol. 22 36 rds. = 594 ft. (28 in. + 18 in.)+-2=23 in. average width 594 ft. X4 ft. xf| ft. = 4554 cu ft., x $.28 = $1275. 12. More exact solution : 594 ft. x f J ft. = 1386 sq. ft. ; 594 ft. X . = 891 sq. ft. 1386x891 = 1,234,926. \1234926= 1111.27 sq. ft., + 1386 sq. ft. + 594 sq. ft. = 3388.27sq. ft. 3387.27 sq. ft.x4 ft.xj = 45176.9 i- cu. ft., (vol. of pyramid) x $.28 = $1264,953. 23 594 ft. x(|f+^)ft. = 1584sq. ft.,x T \ ft. = 1056cu.ft.,x$.32 = $337.92. 24 3.12 in.x3 in. x =5.43 sq. in. area of one triangle, x 8 = 43.44 sq. in. area of base. 43.44 sq. in. x 120 in. = 5312.8 cu. m.,-r 1728=3.0745 + cu. ft. MISCELLANEOUS 141 MISCELLANEOUS 261 Pae 257. = $220.50. 2 $1714.275-r$1.425 = $1203. 7 x 30 x $2 + $27 = $447. $1203 - $447= $756,-J-210= $3.60. 3 Amt. of $1 at C. Int. for five years =$1.343916. $5000 -r $1.343916 = $3720.47. 4 800 x $4.75 = $3800, x .Olf = $66.50 com. $3800.- $66.50 = $3733.50, -r 1. 02 = $3660.29-7-. 06 J= 56312 Ib. $3733.50 -3660.29 = $73.21 com. $66.50 + $73.21 = $139.71 5 4 A.xl60 = 720sq. rds-r-(9x5) = 16 sq. rd. V16=4. 4 rd. x 5 = 20 width. 4 rd. x 9 = 36 rd. length. (20 rd. + 36 rd.) x 2 = 112 rd. x 16 J = 1848 ft. dist. around field. 1848 ft. -7- 8 ft. = 231 number of posts required 1848 ft. x 8|ft. = 15,708 ft. close boards. 1848 ft. x 2 x 4-r 12 x 2 = 2404 ft. scantling 231 ft. x 8x5x5-7-12= 3850 ft. posts. 32.022 M. $440.44 -r 22.022 =$20. 6 327.46 ares-r 3 = 109.15^ ares x 100 = 10915 sq. mi. V10915 = 104.48 -m. wide. 104.48x3 = 313.4+ m. long. 7 8 17ft. 204in.-r39.37 = 5.1816 m. 13ft. 2 in., = 158 in.= 4.0132 m. 5.1816 m. x 4.0132 m. = 20.791 sq. m. x .85 = $17.67 142 MISCELLANEOUS 9 5.13875 mi. x 320+ 25.312 rd. = 1669.712rd,x 5^ = 9183.416 yd. -147.3125 yd. =9036.1035 ft., x 3 = 27, 108. 31 ft. 10 124 2 = 153.76sq. m.x3f=483 sq. m.-j-100 = 4.83 ares. 11 36 A. x 160 = 5760 eq. rd. 4- (9 x 10) = 64 sq. rd. V64= 8. 8x9= 72 rds. width. 8xlO = 80rds. length. 72 rds. (1188 ft.) x 60 ft. x 2= 142,560 sq. ft. for 2 streets. 80 rds. (1320 ft) x 80 ft. x 3= 316,800 sq. ft. for 3 streets. 142560 Bq. ft. + 316,800 sq. ft. = 459,360 sq. ft. for streets 36 A.x 43,560 sq. ft. =1,568,160 sq. ft. -459,360 sq. ft.= 1,108,800 sq. ft. 12 36A.x$500=$18,000 + $800=$18,800. $42,240- $18,800 = $23,440 gain. $23,440-7- $18, 800 = 124|f %. 13 220xl.08| = $239.25. $500 -$239. 25 = $260. 75 -7- $239. 25 = 109%. 14 278.54 ares x 100 =27,854 sq. m.-;-. 7854 =35, 464. 73 sq. m. V35, 464. 73 =188. 32m. 15 $54-r.01|= $3000. $3000-7-3000 = $1 per cental. 16 $1.00-.01=.98f. $.98^-7- 1.025 =.96 invested from each dollar. 1.00- .96=.04 k com. $241. 40 -=-.04 =$6035. $6035 x .96= $5793.60 cotton investment. 17 $1 of note cost me$.66f x 1.25= $.83J,x. 95 = $.79 proceeds. $.79 proceeds- $.66J cost=$.12 gain. $75x .12J = $600 face of*note. MISCELLANEOUS 143 18 8 hr. : 10 hr. 1 40 da. : 60 da. V : : 4 men ; (15 men). 1:2 ) 19 I % rd. x 5 j rd. = 30J sq. rd. 20 34.28 ares x 100= 3428 sq. m.-H of 39.4 m.) = 174.01 m. 21 1 mi. sq. = 640 A.-r2.47 A. = 259. 11 + ares. 22 $3600 X 1.30 = $4680 marked price. .90 x .95 = .855. $4680 x. 855 = $4001.40. 23 $1 + .01 premium = $1.01 - .01 interest = $1.00. 502.25 x$l = $502.25. 24 f- T V=M; 3 + = 3f ; 25 7 + 11 = 18. A's share =;& of 540 A. = 210 A. B's share = H of 540 A. = 330 A. 26 (3.64 m.)' x 3.1416= 41.62494336 sq. m. surface. 3.64 3 =48.3287 + cu. m. x .5236=25.3049 cu. m. 27 80 $1.75 = $140 amount he would have received. $140 - 80 = $60 amt. loss -r ($1. 75 + $. 75 daily loss) = 24 day s loss. 80 da. - 24 da. = 56 working days. 28 |A. = fB. A's=$B'B-hf = fcB's. f B's + f B's=-^ B's = 136yrs. B's=136-r-17 = 8. A's=8x8 yrs. = 64yrs. s = 8x9 yrs. = 72yrs. 29 2.8 2 x .7854= 6.1575 + eq. m. area of base, x 3.8 = 23.3985 cu. m. x 1000=23,398.5 litres or kg. 144 MISCELLANEOUS 30 I of quantity = 56 A. 18 sq. rd., -f 4 A. 126 sq. rd. = 60 A. 144 8q. rd. A's share. Quantity - A's share = 388 A., x = 77 A. 96 sq.rds. B's share. 388 A. - B's share = 310 A. 64 sq. rd. x = 103 A. 74& sq. rd. C's share. 310 A. 64 sq. rd. - C's share = 206 A. 149 sq. rd. D's share. 31 Dist. around=5 rds.x4=330 ft. (length) x 3 ft. ( width) + 3 ft. x 3 ft. x 4 (comers) = 1026 sq. ft. Vol. of earth = 5 rds. x 5 rds. x 6 in. = 3403^ cu. ft. 3003 J cu. ft. H- 1026 sq. ft. = 3.3168 + ft. deep. 32 43.6 m. x 27.9 m. x .16 m. = 194.6304 cu. m. x 1000= 194,630.4 kilograms. 33 10 a x. 7854x10 = 785.4 cu. ft. x 1728 = 1,357,171.2 cu. in.,-*- (63x231 cu. in. = 14,553 cu. in.) = 93. 257 hogshead. 34 1 = $4.866,-:- 20= $.243 value of shilling. $l-^$.243 = 4 s. 1.38 d. value $1. 1 fr. = $.186. $l-7-$.186=5.376 fr. value $1. 35 58.248 cu. m.^ (3.7 m.x 3.42m. = 12.654 sq. m.) = 4.6+ m. 36 550 X $1.80 = $990, X 1.02 J- = $101 2.275, + $17 = 1029.275, x 1.00^ = $1031.848+. 37 $750=| prin. Prin. = $600. Int. $150. Int. on $600 3 yrs. @1% = $18. 38 32.5 m. x 3.2 m. x 1 '8 m. = 187.2 cu. m., or steres. MISCELLANEOUS 145 39 3| days+ 14 J- days = 18 days. $53-j-18 = $2.94f per day. 3x$294f = $10.3055 share of one. 14|x$294f = 42.69f share of other. 40 of $5400 = $1800 C's share. 8000 + 10,000 = 18,000. A's share = T V B's share = }. $5400 - $1800 = $3600. T \ or f of $3600 = $1600 A's share. 10 or | O f $3600 = $2000 B's share. 41 52 men : 45 men 15 da. : 25 da. 42 $3.50 C. xl.20 = $4.20 S. P., -i-. 80 = 5.25 A. P. 43 8f cd. x$7.20 = $63.36-r(.20+.12) = 198 Ibs. of each. 44 2.28 m. x3f = 7.!6i m. circum. 3.8 2 m. + 1.14 2 m. = 3.96 in. slant heighth. 3.96 m.x7.16 m.xi = 14.l877 sq. m. surface of sides 2.28 2 x .7854 = 4.0828 sq. m. area of base. 14.1877 sq. m. + 4.0828 sq. m. = 18.27 sq. m. 45 729 = 3,3,3,3,3,3. 336=2,2,2,2,3,7. 1836=2,2,3,3,3,17. 46 $2675 - $2225 = $450. 180 sheep : 1500 sheep : : $450 : ($3750). 47 336(84_G. C. F. 420(84_G. C. F. 504(84_G. C. F. 336(4 420(5 504 (6~ 48 32.5 m.x32.5 m.x 1.8 = 187.2 steres,-r.276 cd.=51.66 cd. .66 cd.x 188 = 83.48 cu. ft. 146 MISCELLANEOUS 49 $60xfxf = $54. 50 fof42Dgal. = 262Jgal. + 87} gal. = 350 gal. 350~420=f. 51 24 T. 4 cwt. 1 qt. 18 lb. = 54,254 Ib.xS d. = 162,762 d.x .020J = $3295.93 cost. 54,254 lbs. = 24 2 ^ S. T.x$142 = $3852.03 S. P., - 3295.93 C. = $556.10 G. 52 38.18 m.x73.3 m. x .003 m. = 8.395782 cu. m. = 8395.782 kilograms. 53 Diff. in time = 6 mo. 17 da. Int. on $1 for given time $.0655. $714.50 x i.065f =$761.418. 54 $534x1.04 = 555.36 amt. of note. Discounted time from Mar. 17 till June 4 = 2 mo. 17 da. $555.36 x .021^ = $11.879 discount. $555.36 - $11.879 = 543.441 proceeds. 55 At one o'clock hour hand is 5 minute spaces ahead of minute hand, and will be overtaken by minute hand in T ! T of 5 minutes, or j\ min. Hence, Ans. 5 T 5 T , min. past one. 56 tV f CO min. = 4 T 8 j min. Hence at 55y 5 y minutes past twelve, cr at 4/j minutes to one o'clock. 57 The principal due each year will be the present worth of the principal for the proceeding year. 1.10)$1.00 1st. P. W. 1.10) .90909 2nd. " 3.10) ^82644 3rd. " 1.10) .7513 4th. " 1.10) .683 5th. " 14.1697 total P. W. $5000^- $4.1697 = $11 99.08 amt. of each payment. APPENDIX ANSWERS TO PRIMARY NUMBER LESSONS NOTE. Very few of the examples in the Primary Number Lessons are numbered in consecutive order, nevertheless the careful teacher can easily place the answers as found in this Appendix. 12 14 16 20 22 7 25 3 5 Page 19 Page 20 Page 22 Page 97 Page 29 7 5 Page 32 o 1 3 1 *- / 7 4 4 3 2 2 1 1 1 5 2 2 4 1 4 5 3 1 1 3 1 2 5 1 7 1 3 7 7 i 2 6 4 6 2 6 4 4 2 7 8 1 27 Page 34 6 5 3 2 2 3 5 6 1 8 1 2 3 4 2 5 7 2 2 7 6 3 Q i 3 5 1 1 1 1 1 7 5 24 Page 7 7 O 5 5 7 31 8 13 Page 15 Page 18 Page 21 G 1 8 7 6 1 19 2 5 21 2 3 24 5 2 Page 28 4 23 Page 30 G rt i 4 26 Page 33 3 6 1 30 5 5 9 4 3 1 5 Page 3 4 40 1 3 3 7 4 36 * 4 1 3 5 1 6 J 5 1 4 2 3 6 7 4 4 2 3 2 7 4 3 5 1 6 3 " 28 Page 34 8 9 6 1 2 2 6 3 4 8 1 2 1 2 2 2 5 6 5 6 1 3 5 1 4 5 1 (147) 148 APPENDIX 6 34 36 9 2 44 6 3 2 5 Page Page 2 10 Page 2 5 3 7 40 41 3 1 50 2 2 2 2 3 6 6 2 5 4 2 o fi 1 6 3 6 9 2 1 3 4 4 9 w 7 7 G 3 3 8 9^ 42 Page 48 1 2 3 3 2 3 8 10 3 3 4 2 2 52 31 Page 37 6 3 8 (p. 42) 5 2 5 1 4 5 A 2 5 3 2 4 9 50 Page 58 2 4 4 6 4 3 Page 8 1 2 3 8 8 5 56 3 2 1 6 39 10 1 : 2 1 9 4 5 2 8 Page 1 7 2 6 48 3 2 3 1 7 7 3 2 Page 2 6 2 2 2 55 10 6 8 37 9 9 45 6 2 8 4 Page 5 4 Page 4 10 5 9 3 42 2 6 51 8 4 8 9 4 4 3 4 6 9 5 1 5 3 3 5 4 9 7 6 9 2 3 10 7 10 4 5 53 3 32 Page 38 35 Page 41 6 3 9 9 2 1 3 3 9 8 6 43 Page 49 4 5 2 1 6 2 7 9 8 2 1 2 3 2 4 2 Page 59 5 9 10 5 |B : 1 5 2 6 8 6 4 5 2 1 6 4 7 3 l/ 5 3 49 51 12 3 3 3 1 4 Page Page 6 4 9 i 8 7 55 57 6 4 8 7 2 1 5 i 3 1 40 Page 7 3 9 3 3 5 6 2 3 5 4 4 5 2 5 7 8 7 5 38 Page 43 TTtJ 3 5 10 1 2 1 6 46 Page 52 3 4 9 9 5 4 2 3 4 5 1 2 7 2 4 1 10 7 4 10 3 8 9 3 10 8 3 3 3 9 7 4 4 5 5 2 4 6 2. APPENDIX 149 54 2 17 62 5 73 11 60 Page 4 14 Page 7 811 9 30 60 3 11 69 2 912 5 19 2 (P. 64) 15 16 8 1 2 1015-3 11 8-4 8 3 35 25 19 8 5 12 2 7 33 7 14 4 2 13 8 6 28 : 7 2 14 3 2 5 2 5 5 4 12 (p66) 16 1Q 4 5 5 4 8 3 10 15 6 1616 1714 18 9 12 4 4 14 72 Page 86 4 8 3 3 o U 7 5 3 5 5 O5 CO 00 1C T H T-H i-H t-H T-H T- 63 Page 70 65 Page 73 7 19 1 3 10 9 6 8 8 8 6 2 Col's 51 42 35 40 A A~X 1 e 6 4 12 39 q 58 1O 8 4 2 69 40 o 55 Page 65 2 15 16 15 2 2 Page 82 48 47 Page 61 6 8 5 5 61 Page 68 5 6 2 15 17 4 6 14 5 16 1 18 9 4 9 39 34 Sub'n 2 5 13 15 4 8 Omit 6 1 6 2 7 9 1 4 4 2 2 10 9 9 7 8 19 12 9 2 1 6 16 8 8 2 18 10 Q 2 4 4 8 14 4 2 8 3 ^t 4" 7 7 7 q 4 10 4 3 8 5 1 2 7 1 10 3 t/ 11 4 9 2 q 11 7 5 9" 4 9 2 O fi 10 2 3 3 4 5 u 1 4 4 2 2 5 Review 9 1 7 57 59 Page 10 3 5 3 64 TpQryo Page 77 115 68 Page 71 Page 84 73 Page 88 o 65 8 Page 215 80 2 DO 5 / 1 312 Col's 5 3 13 5 2 4 3 15 47 7 8 18 8 2 514 3 59 4 10 14 2 2 610 6 20 13 150 APPENDIX 2 75 78 83 90 91 Col's 3304 13 Page Page Page Page Page 3237 3626 3 90 94 101 112 114 892 1035 9 952 852 4 3 Cols 7Q 8 9 Col's 249 7ft 245 389 557 1809 1078 3320 17 11 / o 58 er\ 7 26 35 42 / o 191 1 1 Q 88 199 subt. 5364 2340 3 ou CO 18 49 llo 1 1 A 88 263 " 5357 15 53 />rv 13 47 119 116 659 3656 14 bO 23 43 /N 14 86 476 4590 PnPa 51 Kfi 5 40 Col s 538 366 3960 \j(ji a crv Ov CA 13 41 1340 159 25 348 ou Arj oy co 13 39 469 546 89 2067 47 40 CO 52 60 (P. 93) 37 1301 617 377 477 173 480 2653 3184 Oo Af> subt. z oo 572 53 158 2502 rto 51 50 K1 omit'd (p. 91) I Q 81 Oy Page 111 555 (pH3) 213 29 147 172 374 57 587 5477 276 2095 Ol 35 50 74 Page 89 46 91 40 18 3 3 12 14 15 4 7 2 9 Page 98 6 12 27 8 15 2 9 637 549 454 569 517 478 406 665 454 e Art 181 522 123 231 712 102 314 624 635 340 498 454 279 165 133 89 285 304 8038 3664 458 395 372 67 2iO 149 32 38 214 10 13,456 409 (P H7) 4473 8385 2750 28,931 3038 70 12 OUU. 205 19,476 99 subt. 34 47 77 "POO 1 *! 22 20 546 70 414 512 11,672 6858 576 263 174 41 .rage qq 2 /o AQ 744 4803 652 69 vo 13 rty 513 127 11 77 62 68 Col's 78 68 24 27 21 10 47 6 (p.112) 520 506 96 40 92 Page 114 93 Page 116 250 1 101 83 21 67 15 12 66 1 1 qx 2148 371 72 62 6 11 5 11OJ OAAO 4368 344 78 49 9 6 12 2903 99 5628 383 6 39 3 3 4 & 516 536 42 43 18 24 10 (pH5) 5016 116 44 53 12 68 120 4800 1724 259 5 46 2 58 99 250 3069 378 31 45 12 10 70 156 675 483 APPENDIX 151 243 142-1 $825 216,909 103 133 522 90-5 52 hrs. . 62,444 Page 129 6 477 64 21 bbl. 92,542 J K 5 608 76-1 126 26,662 o in 8 638 92 61-2 197-3 11172 Review & JLU 318 A 66 22 94 Page 117 $1.68 280 16-5 71-4 33 43-1 279-1 6889 1836 366-3 2472 7612 Page 124 146 21 ct. 354 4 (\ 4 6 5 9 6 4 724 8 7 106 Page 133 $6.76 322 980 (p. 118) $1940 1872 1^ 49 62-2 36-2 47-1 85-2 82-5 Ot? 98 Page 122 849J 237} 4 9 5 6 6 5 727 856 9 5 10 8 104 Page 130 1 1 2 2 3 5 116 221 310 424 5 3 615 / 7 4 oO 45-2 87-9 oa A 932f 243f 1128 19 J20c. 12 J25 c. 496 5 W 610 748 8-8 960 11 5 7 34 4 8 7 OD ^ 86-3 85-1 58-2 358 83-3 94-3 57-6 79-1 39c 973J 753 T 8 r 493 T V 489 13 $24 14-$6 15 9y's 100 Page 125 128 218 7 8 875 910 10195 27,189 69,247 62,048 87,720 1012 1st .Col. 36 96 35 24 - 77 18 4 72 52-5 53 48-8 99 Page 123 321 4 4 5 4 105 Page 132 24 36 45 77 47-2 110 6 6 Last Set 77 63 23-6 2 2 724 3 42 144 39-1 3 7 8 6 12 2 58-1 4 6 954 27 2nd Col. 3 76-3 5 5 1036 5 6 62-1 6 7 63 7 24 70 7 5 119 4 62 60 96 810 9 48 32 6 Page 119 9 6 10 7 7 15 6 6 91 60 Q c $4375 11 5 8 8 40 99 Page 119 25 doz. 15 p'ncil 12 6 (p. 124) 52 95 132 25 27 42 79-3 (p. 120) 13 3 132 6 16 56-8 150 yds. 47,801 11 6 65 >Z APPENDIX 3rd. Col. J 520 cts. 7-7 42 1-1 6 - r 835 63 2 2 M 94 16 O 4 8-r 2 r 109 40 12 fcl 9-li 10 * 11604,192 12290,796 42 112 l ? 1326,232 12 44 Page 1QQ 14 5934f 15-76 15 J.OO H 1611 42 17 2 cts. 16 cts. 110 Page 2 if 3 H 4 11 A i 188. 1921 206 136 -1 4 217 i 20 642 2224 A A\J 256 325 430 525 618 IT Q 8 5| 9 2J 104* i i_ 2nd. Col. TV 237 2448 259 26-61 2720 cts 287. 860,000 942 1095 45 i at 24 j! 2949 304 3143 325006 96 24 *T 3rd Col. QO_ / 24 > 6 90 33 ~ 110,972 3446,717 60 2 | 3525,326 \j\J 72 00 if 1 3672 378 oo fifi T 64 T V 388 oo 5 03 397 111 1 11 ? 4014 414 4212 7\ A 435 ^ 'TI i 9 r 449 2 1 113 Page Rev. Page 141 19 feet. 4521 4612 47-f 4 236 48-4A 2 1 A- 328 49-7 } 2 | 4 $1 50 3 3 i 52 5118,564 1 4 j- 632 528372* " / OF . . APPENDIX 153 53159,637 90134 (31,246| 54- \ 7 1>HI 91-i 9230 125 -|28,754| f 16,827f (334,825 ]242,779 936| 94 53 12629,285 127 5,720 5616 9530 12812 cts. 57 - 6 /-, V> 967 12924 cts. 5848 cts. 975 130 117 sq. ft 59 5 days 982 1314 days 6088 9930 1325 hrs. 6112 1006 13311 628 ( 23,456f 13411 6312 10 , ) 54,321 135114 648 } 7j 392j 6 T 1367 6538 ( 12,468^ 13730 661 J690,760 ( 7,891f 673579^ 1 34,150 138 \ 19,465 ( 65,791 (351,845 (l5 864^ 68 i 129,070 I 74,976 103 i 27,158 1481,382 1399 140 19J 6918^ 104653,584 141 4f 7033 J05 18 14257 7114 10610 cds. 1439 7211 10754 j 7>293J 7332 1081 (13,597y 742| 10912 1183,750 (31,884 no- A 58,583 75 -^ 91,877 11160 195,276 121,816 11254 982 ( 29,259 1134 236,407 76^101,940 { 87,199 11410 11524 147 (6,879f -L*< " ^Q OO'Tll 77 -V 11611 1482 7816 11767 149 16 7924 1185 cts. 150 -\ 6 -, Y 8040 cts. 11945 151 6p'nc'ls2c ( 9,631| 120 $4.80 152 $48 81 j 2,486f 82 6000' ' (581 121^ 15f (48| 153 $.71f 15484 155 If 8399,534 12221 1566 845 (468,305 1574 858 123 \ 34,619 1585 8654 / 54,185 159 14U 8715, 27 8917 ( 55,926 24 ^ 33,741 1449,184 16015 161-6 T \ YB t 7