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 1 2 3 
 
THE NEW ARITHMETIC 
 
 COMPILED BY 
 
 THREE HUNDEED PROMINENT EDUCATORS 
 
 AND EDITED BY 
 
 SEYMOUR EATON, 
 
 Author OS Eaton's Practical Grammar, and Editor of the School Supplement. 
 
 TORONTO: 
 
 EATON, GIBSON & CO. 
 
 1885. 
 
Entered, according to Act o{^ Parliament ot Canada, in the year one thousand 
 eight hundred and eighty -five, by Eaton, OiBSO^f & Co., in the ice of the Minister 
 of Agriculture at Ottawa. 
 
 Tia^ 
 
 FIUNTKD AT THE CHRISTIAN GUARDIAN OFFICE, TORONTO. 
 
EDITOR'S :^OTE. 
 
 The contributors to tho exercises in this book are about three 
 hundred in number. The names of those from whose contri- 
 butions I have drawn most largely are adjoined. I am myself 
 responsible for the plan of the work, for the grading, and for 
 a large number of the exercises. Explanations of theory, and 
 other introductory matter, which the teacher should himself 
 provide, I have purposely omitted. I have endeavored to pre- 
 pare a pupUs' hand-book. The practical character of the exer- 
 cises will commend them to all who nave at heart the mental 
 development and the business success of their pupils. I have 
 Avoided all exercises requiring much labor and affording very 
 little intellectual or practical benefit. The work of the ele- 
 mentary departments prepares the pupil for the study of alge- 
 bra, geometry, and the higher mathematics, while the more 
 advanced work prepares him for the active duties of everyday" 
 life, and at the same time gives him such mathematical train- 
 ing as he may not have time to secure in any other way. 
 Suggestions and criticisms are solicited. 
 
 Toronto, May, 1885. 
 
 SEYMOUR EATON. 
 
CONTRIBUTORS. 
 
 Pbof, D. E. Lantz, 
 
 Mathematical Moater of the State Agricultural College, Manhattan, Kan. 
 William Marigold, 
 
 Head Master of the National School, Chippenham, Wiltshire, England. 
 W. H. Sims, 
 
 Superintendent of Education, Goshen, Ind. 
 John Tait, 
 
 Mathematical Master of the Collegiate Institute, Colllngwood, Ont 
 W. A. Beer, 
 
 Principal of Callensburg Academy, Callensburg, Pa. 
 E. P. RowELL, M.A., 
 
 Head Master of the Grammar School, Sacramento, Cal. 
 N. SOMERVILLE, 
 
 Superintendent of Education, Sherman, Texas. 
 Mrs. Mary R. McGwigax, 
 
 Principal of the High School, Charieston, W. Va. 
 Miss J. H. O'Neal, 
 
 Assistant Principal of the Public Schools, Falls City, Neb. 
 S. G. Pryor, 
 
 Principal of F. Girls' School No. 21, Baltimore, Md. 
 S. E. Grover, 
 
 659J Congress Street, Portland, Me. 
 W. S. Ellis, B. A., B.Sc, 
 
 Mathematical Master of the Collegiate Institute, Cobourg, Ont. 
 Principal D. H. Burbidge, 
 
 Public Schools, Halifax, N.8,. 
 W. J. Robertson, B.A., LL.B., 
 
 Mathematical Master of the Collegiate Institute. St. Catharines. Ont 
 E. M. Bigg, B.A., 
 
 Priucipal o* the High Schof J, Parkhill, Ont. 
 
:j:.T3su4-^aiKafca^;ic^aBaE'.i»BW 
 
 wmmm 
 
 VI 
 
 CONTRIBUTORS. 
 
 M188 Sarah M. Tayix)^, 
 
 Practice School, Portland, Me. 
 
 T. M. Henry, B.A., , 
 
 Mathematical Master of the High School, Belleville, Ont. 
 
 Michael O'Brien, 
 
 Head Master of the Roman Catholic Separate School, Lindsay, Ont. 
 
 D. F. A. WiLKiNS, B.A., B.Sc, 
 
 Mathematical Master of the High School, Mount Forest, Ont. 
 
 E. J. Garrison, A.B., 
 
 Principal of Union City District High School, Troy, Tenn. 
 
 Prof. D. D. Cottrel, 
 
 High School, New Bremen. N.Y. 
 
 Prof. J. A. Cox, 
 
 Principal of the State Normal School, West Liberty, W. Va. 
 
 William A. Peck, A.M., 
 
 Superintendent of Education, Whitestone, Long Island, N.Y. 
 
 B. Bavin Hardy, B.A., 
 
 Heai' Master of OaltleV School, Church Road, Bournemouth, Hants, Eng. 
 
 M188 Clara '7illino, 
 
 Institv.te of Holy Angels, Fort Lee, N.J. 
 
 J. Wollman, 
 
 Head Master of Wellgate Board School, Rotherham, England. 
 
 W. P. GouDiK, B.A., 
 Derby, England. 
 
 Michael O'Kelly, 
 
 Head Master of Louisburg National School, Westport, Ireland. 
 
 Edward Allen, 
 
 Head Master of Rushen School, Isle of Man. 
 
 Thomas W. Halfhead, M.A., 
 
 Grammar School, Colne, England. 
 
 James W. Elliott, 
 
 Principal of the Normal School, Cassville, Pa. 
 
 William Grant, CM., 
 
 Head Master of the Public School, Farquhar, Dornoch, Scotland. 
 
 Prof. J. W. V/eiton, 
 
 Principal of the Business College, Grand Rapids, Mich. 
 Prof. D. Lewis, 
 
 Superintendent of Education, Fairfax, Mo. 
 
 Principal F. Clarke, 
 
 Public School, Sanborn, Dak. 
 
CONTRIBUTORS. 
 
 Vll 
 
 Miss Mary E. Wells, 
 
 216 8. Prospeot St., BurHngtoin, Vt. 
 Miss Nellie E. Chapin, 
 
 Goodale's Corner, Me. 
 
 Principal John L. Hall, 
 
 Public School, Shlpman, 111. 
 
 Richard Lees, 
 
 Principal of the Model School. Dndtay, Ont. 
 Dr. J. W. Carlylb, 
 
 Mathematical Master of the Provincial Normal School, Toronto, Ont. 
 M. JuDsoN Vincent, 
 
 MarcelluB, Mich, 
 
 C. A. Fleming, 
 
 Principal of the Northern Business Collejfe, Owen Sound, Ont. 
 Miss Edith Etheridoe, 
 
 Paghan National School, Bognor, Sussex, England. 
 John Shaw, 
 
 British School, Hollingworth, Manchester, England. 
 Thomas Kirkconnell, 
 
 Mathematical Master of the High School, Vankleek Hill, Ont. 
 Thomas Kenny, 
 
 Orlar National School, Kilkelly, Co. Mayo, Ireland. 
 TaoMAS Watts, M.C.P., 
 
 College School, Cambridge House, Baldock, England. 
 Principal A. Nesbitt, 
 
 92 Meclenburg Street, St. John, N.B. 
 Anna Riland, 
 
 High School, 81 Jefferson Street, Dubuque, la. 
 B. F. Hoover, 
 
 Superintendent of Education, Smithviile. Ohio. 
 Prof. H. A. Sherman, 
 
 307 East 9th Street, New York City. 
 Peop. a. R. Martin, 
 
 School Examiner, Gavers, Ohio. 
 J. T. Slater, 
 
 Principal of Parliftmcn*. Street School, Toronto, Ont. 
 R. R. Jennison, 
 
 Principal of the West Ward School, Barrie, Ont 
 Samuel Price, 
 
 Head Master of Wedmore National School, Somerset, England. 
 
viii 
 
 CONTRIBUTORS. 
 
 Miss Hattib L. Finlak, 
 
 Trove School, New Bedford, Mms. 
 Db. N. H. Tarrant, 
 
 1824 Ellia Street, 8»n Franolwo, Cal. 
 G. H. Howard, 
 
 Principal of tlie Oraiiima.' School, Berthier en Haut, Que. 
 Pbof. S. D. Waterman, 
 
 Prinjlpol of the High School, Stockton, Cal. 
 Miss Euzaleth Lkks, 
 
 Ottawa, Ont. 
 
 Principal H. MoKinly, 
 Clintonvllle, Pa. 
 
 Miss Elizabeth A. Sorin, 
 
 1006 North Lofflngwell Avenue, St. Louii, Mo. 
 J. W. Westfrvelt, 
 
 Principal of Woodst-Xik Business College, Woodgtock, Ont. 
 Charles W. Harris, 
 
 Head Master of the Bfcard School, Tregoney, Cornwall, England. 
 Miss Juliet Porter, 
 
 11 E. Shelby Street, Worcester, Mas«. 
 Wallace Rodoers, M.A., 
 
 Principal of Victoria Grammar School, Melbourne, Australia, 
 Miss Emma T. Wooden, 
 
 66 Sunmer Street, Rochester, N.Y. 
 Prof. W. F. Smith, 
 
 Principal of the Public School No. 5, Baltimore, Md. 
 Principal G. E. Stokes, 
 
 Corinth, Miss. 
 
 R. F. Greenlees, 
 
 Principal of the Public School, Bracebridge, Ont, 
 John Campbell, 
 
 Principal of Ardallie School, Aberdeenshire, Scotland. 
 Principal J. A. Wilmot, 
 
 17 Woodbine Street, Cleveland, Ohio. 
 
CONTEI^TS. 
 
 First Department. 
 
 Paoi 
 
 I. Addition i j 
 
 II. Subtraction ly 
 
 III. Multiplication 20 
 
 IV. Division . . . 2ft 
 
 V. Revi'iv oi 
 
 Second Department. 
 
 I. Factors and Multiples 41 
 
 II. Common Fractio'js 44 
 
 III. Decir. j,l8 g2 
 
 IV. BusineBS Exercises 55 
 
 V. Rovisw go 
 
 Third Department. 
 
 I. Measures g- 
 
 II. Currency i^j 
 
 III. Wages y^^^'^y^^..^'.]'.'.'.'.'.'. 74 
 
 IV. Bills and Accounts >jq 
 
 V. Review 04 
 
 Fourth Department. 
 
 I. Surface Measurement 91 
 
 II. Solid Measurement 93 
 
 III. Lumber Measurement , 95 
 
 IV. Building and Furnishing gg 
 
 V. The Metric System " 2OO 
 
 VI. Review jP2 
 

 CONTENTS. 
 
 Fifth Dzpartmbnt. 
 
 Page 
 
 I. Percentage , , ^ 
 
 II. Trade Discount " j la 
 
 III. Invoices * " ,0^ 
 
 IV. Commission ,09 
 
 ^' Taxes ..........".".'.'.'.'" 126 
 
 ^^' ^®^i«w 12» 
 
 Sixth Department. 
 
 I. Interest ^.^^ ,03 
 
 II. Commercial Paper 1^4 
 
 III. Bank Discount jgi 
 
 IV. Partial Payments ..." 15.^ 
 
 V. Review , -';, 
 
 Seventh Department. 
 
 \ 
 
 1, Stocks and Bonds joi 
 
 II. Exchange , ,„ . 
 
 III. Insurance ' j^,, 
 
 IV. Bankruptcy ,qj 
 
 V. Partnership jgg 
 
 VI. Square Root ' |-.q, 
 
 VII. Review * , -, 
 
 Eighth Department. 
 
 Examination Exercises i^a 
 
THE NEW ARITHMETIC. 
 
 FIEST DEPAKTMENT. 
 
 I. ADDITION. 
 
 HINTS AND DEFINITIONS. 
 
 tJ!!^f^^.^' amount of two or more numbers is the number equivalent to air 
 the units of the given numbers. 
 
 The sign of addition is + . it is read phis. 
 
 The sign Of dollars is ^ it is read dollars. 
 
 The sign Of equaUty is = . it is read equah, or is equal to. 
 
 Write the numbers in vertical Unes. irregularity in the placing of figure* 
 18 the cause of many errors. «i"«co- 
 
 TlUnk Of resultw, and not of the numbers themselves. Thus, do not say 4 and 
 5 are 9, and 6 are 15, and 7 are 22, etc. ; but 9, 15, 22, etc. 
 
 Make combinations of lo or other numbers as often as possible, and add them 
 as single numbers. Thus, in adding 9-34 7-3 2179 54 82113, say 9, 16, 26, 33, 42. 51. 
 61, 67, taking each group at a glance as a single number. When a figure is repeated 
 several times, multiply instead of adding. repeaiea 
 
 In adding horizontaUy. begin at the left, since the eye is more accustomed 
 to mov.nf; from left to right than from right to left. ""^tusTOmea 
 
 to adding long COlumnb, prove the work by adding each column separately 
 in the opposite direction before adding the next column. 
 
 EXERCISES FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 1. Find the sum of 24, 26, 37, 85, 63, 42, 21, and 13. 
 
 2. Find the sum of 37, 201, 402, 42, 25, 101, and 202. 
 
 3. Find the sum of the numbers between 9 and 20. 
 
If 
 
 \ 
 
 12 
 
 FIRST DEPARTMENT. 
 
 4. Find the sum of all the numbers ending with 5 between 
 10 and 60. 
 
 6. Find the sutn of the four numbers that can be expressed 
 by the figures 3 and 5. 
 
 6. Find the sum of fhe four numbers that can be expressed 
 by the figures (> and 9. 
 
 7. Find the sum of all the numbers from 12 to 48 inclusive. 
 
 NoTB—When numbers are In regular arithmetical order, as 3, 4, 5, 6 or 2 4 6 
 8. or 5, 10, 15, etc., to find their sum, add the first and last, take half, and multiply 
 Dy the number of numbers. The half-sum represents the middle or average number. 
 
 8. Find the sum of all the even numbers between 1 and 101. 
 
 9. Find the sum of all the numbers from 3 to 37 inclusive. 
 
 10. Find the sum of all the odd numbers between 50 and 100. 
 
 11. Find the sum of all the numbers ending with 5 between 
 1 and 100. 
 
 12. Find the sum of all the numbers from 1 to 999- inclusive. 
 
 13. How many days in the summer months ? 
 
 14. How many letters will it take to write 425 iii words ? 
 16. How many letters will it take to write 23,249 in words ? 
 
 WRITTEN DRILL EXERCISES. 
 
 16. How many letters will it take to write 2,304,625 in words ? 
 
 17. Find the sum of the fifteen numbers that can be expressed 
 by the figures 1, 2, and 3. 
 
 18. Find the sum of the fifteen numbers that can be expressed 
 by the figures 3, 5, and 7. 
 
 19. Find the sum of the ten numbers that can be expressed 
 by the figures 2, 5, and 0. 
 
 20. Find the sum of the five numbers that can be expressed 
 by the figures 2, 2, and 0. 
 
ADDITION. 
 
 13 
 
 21. Find the sum of the eight numbers that can be expressed 
 by the figures 2, 5, and 5. 
 
 22. Find the sum of the three numbers that can be expressed 
 by the figures 7, 7, and 7. 
 
 23. Find the sum of all the numbers between 999 and 1201. 
 
 24. Find the sum of all the numbers between 1904 and 3154.. 
 
 26. A man who was born in 1826 died when he was 49 years- 
 old. In what year did he die ? 
 
 26. How long a cord will it take to go round a garden 327 
 feet long and 298 feet wide ? 
 
 27. Add together the six numbers of three figures each that 
 can be formed with 5, 6, and 7. 
 
 7i«f« ^'rtoi?'''" ""^ ^" *^' ""^^^'^ ""*^^"« ^^*^ 789 between 
 7I006 and 82326. 
 
 in?9A ^'^lol;^/"™ ""^ *" *''" ''"™^^"« ""^"^^ ^i*h 55 between 
 10020 and 12001. 
 
 SO. How many years from the beginning of 3984 B.C until 
 the beginning of 1886 A.D. ? 
 
 31. How many days from 12 o'clock p.m. March 31 until 12 
 o clock p.m. January 31? 
 
 32. Find the sum of the five largest numbers that can be ex- 
 pressed by the figures 9, 8, 7, and 6. 
 
 33. Find the sum of the five smallest numbers, of four figure* 
 each, that can be expressed by using the figures 3, 4, 0, and 6. 
 
 34. Find the sum of the five largest and the five smallest 
 numbers, of four figures each, that can be expressed by the 
 figures 9, 8, 3, and 1. '^ 
 
 36. How many times will a clock strike between 11 15 a m 
 and 10.30 p.m. ? ... 
 
 36. The difference between two numbers plus 12 is equal to 
 28. Their sum is 64. Find the numbers. 
 
14 
 
 FIRST DEPARTMENT. 
 
 II 
 lis 
 
 3< 
 
 BUSINESS EXERCISES. 
 NoTK. -Business men and accountanta find it necessary to be able to add readilv 
 rrr "fn "*>!"?? "= * *'°''''''"*'' '^**""' ■" "^" ^^ *^«" ?■-««» - ^ vertli; 
 
 37. Abstract Exercise, 
 
 2345 
 
 1213 
 
 3625 
 
 1625 
 
 1216 
 
 2198 
 
 3621 
 
 6731 
 
 22574 
 
 3542 
 
 214 
 
 2153 
 
 2101 
 
 3120 
 
 25 
 
 982 
 
 5842 
 
 2136 
 
 136 
 
 214 
 
 9876 
 
 2152 
 
 63 
 
 4215 
 
 1563 
 
 1362 
 1043 
 256 
 2136 
 1312 
 2006 
 
 4809 
 2132 
 3429 
 1215 
 2121 
 7849 
 
 2982 i 1215 
 2842 I 1563 
 
 »♦♦»♦ «»•«» 
 
 »♦♦♦♦ «•«»« 
 
 5908 
 
 3621 
 
 1025 
 
 47 
 
 836 
 
 215 
 
 3724 
 
 2152 
 
 3002 
 
 42 
 
 2150 
 
 6 
 
 1098 
 
 46.S5 
 
 2910 
 
 3125 
 
 ♦*»»♦ »««»# «#♦»#♦ 
 
 23723 
 
 •**•* 
 
 ***** 
 *•«** 
 ♦**#♦ 
 ***** 
 ***** 
 ***** 
 
 38. A Week's Mail at a City Post Office. 
 
 Ordinary Letters. 
 Regist'd Letters. 
 
 Post Cards 
 
 Book Packets.... 
 
 Parcels 
 
 Newspapers 
 
 Total 
 
 Mon. 
 
 9243 
 
 659 
 
 2129 
 
 843 
 
 257 
 
 11698 
 
 Tues. 
 
 8564 
 827 
 
 2214 
 
 296 
 
 328 
 
 12325 
 
 **♦## 
 
 Wed. 
 
 9204 
 
 \ 655 
 
 1986 
 
 321 
 
 201 
 
 14276 
 
 Thurs. 
 
 Fri. 
 
 Sat. 
 
 ***** 
 
 7695 7368 9986 
 238 1346 399 
 
 1873 : 989 1655 
 
 655 495 378 
 
 199 ; 276 301 
 
 16883 17319 20205 
 
 »♦»*« **»#♦ ,«»#»# 
 
 Total. 
 
 **«♦* 
 ***** 
 
 ***** 
 ***** 
 
 ***** 
 ****** 
 
 ♦»***♦ 
 
 39. Attendance at an Industrial Exposition. 
 
 
 Men. 
 
 Tues. 
 
 Wed. 
 
 Thufs. 
 
 Fri. 
 
 Sat. Total. 
 
 Children 
 
 Adults 
 
 Single Carriages.. 
 Double Carriages. 
 Officials 
 
 568 
 3625 
 325 
 104 
 210 
 
 496 
 4289 
 204 
 107 
 198 
 
 8653 
 
 15398 
 
 986 
 
 205 
 
 204 
 
 9204 
 
 18327 
 
 805 
 
 124 
 
 179 
 
 769 
 9651 
 142 
 115 
 125 
 
 846 
 
 8984 
 
 121 
 
 m 
 
 113 
 
 ***** 
 ***** 
 #**»« 
 ***** 
 
 
 
 Total 
 
 **#* 
 
 *t'** 
 
 ***** 
 
 »»♦** 
 
 ***** 
 
 
 
 
 
 ****** 
 
ADDITION. 
 
 15 
 
 40. AooKEOATB Attendance at a Public School. 
 
 First Division 
 
 .Second Division., 
 Third Division.... 
 Fourth Division.. 
 
 Fifth Division 
 
 Sixth Division.... 
 Seventh Division. 
 Eighth Division.. 
 
 Jan. 
 
 ; 1040 
 I 1113 
 1214 
 1110 
 1224 
 1316 
 1097 
 1243 
 
 Feb, 
 
 Total. 
 
 ***• 
 
 1003 
 1098 
 1194 
 1201 
 1085 
 1213 
 1109 
 1046 
 
 #»»» 
 
 41. Weekly Report op a Cikculating Library. 
 
 S.^'^^on 762 
 
 History | 321 
 
 Biography | 217 
 
 Science 421 
 
 Poetry 
 
 Religion 
 
 42. Denominational Population of a City. 
 
 WardC. 
 
 Baptist 
 
 Methodist 
 
 Presbyterian 
 
 Episcopal 
 
 Congregational.. 
 Roman Catholic, 
 Other Denora 
 
 Total 
 
 . WardD. 
 
 WardE. 
 1234 
 
 WardF. Total. 
 
 1021 
 
 985 
 
 ♦*#»♦ 
 
 998 
 
 3298 
 
 1063 
 
 «•♦## 
 
 896 
 
 2163 
 
 2054 
 
 «♦•«# 
 
 1542 
 
 3429 
 
 204 
 
 *«##« 
 
 355 
 
 1063 
 
 1365 
 
 ♦*#»# 
 
 1568 
 
 2125 
 
 998 
 
 ♦•### 
 
 843 
 
 899 
 
 1254 
 
 «♦»»♦ 
 
 «»«# 
 
 #♦»»# 
 
 ♦»*# 
 
 
16 
 
 FIRST DEPARTMENT. 
 
 43. A Lumber Mehchant's Sales for One Week. 
 
 
 Mon. 
 
 1 
 
 i Tues. 
 
 Wed. 
 
 Thurs. 
 
 Fri, 
 
 Sat. 
 
 Total. 
 
 Hemlock 
 
 Pine 
 
 12634 
 
 19421 
 
 2563 
 
 4256 
 
 3102 
 
 10563 
 
 242 
 
 14205 
 
 12168 
 
 3146 
 
 2155 
 
 4210 
 
 11369 
 
 563 
 
 15306 
 9121 
 2154 
 1025 
 3214 
 
 15684 
 327 
 
 16214 
 
 10215 
 
 .3214 
 
 2025 
 
 3215 
 
 10025 
 
 984 
 
 18312 
 12056 
 2542 
 3684 
 2156 
 3249 
 562 
 
 20428 
 13206 
 4312 
 5684 
 327 
 2156 
 3428 
 
 «♦#»»• 
 
 Basawood 
 
 
 Walnut 
 
 
 Cherry 
 
 
 Oak 
 
 
 Maple 
 
 
 
 
 Total 
 
 ««*** 
 
 ##♦»» 
 
 •»♦«» 
 
 *#«♦» 
 
 «##♦# 
 
 
 
 #»»»»«. 
 
 44. Columns of Money Items, 
 
 $343 20 $242 15 
 
 $94 06 
 d84 
 
 $327 24 
 
 $643 18 
 
 $321 15 
 
 $493 15 
 
 $*** ♦*- 
 
 24 16 
 
 37 68 
 
 684 19 
 
 36 19 
 
 67 02 
 
 265 14 
 
 *♦* ♦# 
 
 625 13 
 
 8 95 
 
 10 57 
 
 67 68 
 
 204 00 
 
 428 03 
 
 327 18 
 
 ««# #«■ 
 
 84 00 
 
 2 42 
 
 3 68 
 
 3 25 
 
 155 25 
 
 10 00 
 
 242 05 
 
 ««« ««- 
 
 276 05 
 
 37 
 
 19 27 
 
 100 00 
 
 268 13 
 
 100 00 
 
 327 68 
 
 *## «» 
 
 85 
 
 100 00 
 
 242 00 
 
 205 68 
 
 13 17 
 
 256 85 
 
 563 21 
 
 #*♦ ♦» 
 
 27 24 
 
 24 04 
 
 3 24 
 
 35 15 
 
 200 
 
 42 13 
 
 321 14 
 
 »»» #«- 
 
 3 65 
 
 1 or> 
 
 76 
 
 2 14 
 
 30C 
 
 106 27 
 
 124 05 
 
 ««« ** 
 
 276 18 
 
 347 83 
 
 24 93 
 
 75 52 
 
 142 65 
 
 84 27 
 
 245 36 
 
 **# «*- 
 
 «*« *« 
 
 »♦« »» 
 
 »•» #♦ 
 
 »»♦ *» 
 
 *** «# 
 
 #♦♦ *♦ 
 
 *** **■ 
 
 45. Columns of Money Items. 
 
 4t! 
 
 i 
 
 $325 18 
 246 25 
 324 38 
 207 16 
 317 28 
 684 39 
 562 18 
 321 15 
 
 ««» «* 
 
 $201 68 
 
 37 00 
 
 15 25 
 
 68 
 
 .328 14 
 
 29 21 
 
 603 14 
 
 25 18 
 
 $307 16 
 
 27 02 
 
 406 01 
 
 2 00 
 
 26 00 
 308 02 
 
 27 84 
 608 63 
 
 *»# ** 
 
 $204 37 
 
 26 62 
 
 14 08 
 
 ,327 69 
 
 528 20 
 
 98 03 
 
 369 21 
 
 207 18 
 
 *** ** 
 
 $302 15 
 
 3 17 
 
 25 18 
 
 205 69 
 
 25 20 
 
 337 64 
 
 97 25 
 
 427 36 
 
 ##♦ ♦♦ 
 
 $103 42 
 2 08 
 
 2 15 
 
 3 00 
 
 4 00 
 21 00 
 13 20 
 
 75 
 
 ««« «-« 
 
 $614 98 
 
 400 
 
 33 75 
 
 614 00 
 
 22i 00 
 
 95 
 
 8 20 
 
 200 
 
 »»♦ »» 
 
 *** #«- 
 «#* ## 
 
 *»# #«- 
 *** «*• 
 
 .4 
 
SUBTRACTION. 
 
 17 
 
 
 Total. 
 
 s 
 
 «♦»»♦ 
 
 ? 
 
 «««•« 
 
 2 
 
 ««««* 
 
 i 
 
 «*#*♦ 
 
 J 
 
 «««#♦ 
 
 ] 
 
 «»*#» 
 
 i 
 
 •«««« 
 
 h 
 
 #»»*♦* 
 
 $**• 
 ««"» 
 
 *#- 
 
 ## 
 
 *«« 
 
 *«- 
 
 ««» 
 
 ««- 
 
 *## 
 
 «* 
 
 ««« 
 
 ** 
 
 «•* 
 
 *«- 
 
 «*« 
 
 #* 
 
 ««« 
 
 «'N^ 
 
 «»* 
 
 #♦• 
 
 II. SUBTRACTION. 
 
 HINTS AND DEFINITIONS. 
 
 Kivl'lfu^eZno'tZ::^^ ""•"'^" ^^ •^ "-^- -»>•«»>. ^^^ to the ,e«. 
 
 ZZtt TT '"" *'^ "'*''^' *'^ •'"'^'^"^^ '« -"«^ *»>« remainder 
 Subtrac lon is the proce. Of finding the difference between two m^^ls 
 
 The Sign of subtraction is - . it is read minu^ 
 The sun, of the remainder .nd the subtrahend is equal to the minuend. 
 ^ Jhe^d^fference between the remainder and the minuend is equal to the sub- 
 
 BUSINESS EXERCISES. 
 
 -orbinsUL.^r:^r-— -~--^^ 
 
 46. $10 00 -$3 14. 
 
 47. $15 00-12 13. 
 
 48. $30 00 -$9 94. 
 
 49. $10 00 -$7 16. 
 
 50. $20 00 -$2 95. 
 
 61. $5 00 -$190. 
 
 62. $100 -$0 45. 
 
 63. $2 00 -$120. 
 54. $2 00 -$103. 
 66. $7 00 - $2 65. 
 
 66. $40 00 -$23 18. 
 
 67. $25 00 -$15 66. 
 88. $20 00 -$13 21. 
 69. $15 00 -$11 15. 
 60. $50 00 -$22 68. 
 
 .owXT;::riT;TheThretired"r^^^^^^^ rr '-' ^^-- ^« -■ 
 
 papil will put down lhe«n,o„„l„. .1,?^ <l."nne « deHniKi period o( time. The 
 the check, |„ orter o„. .7. ttoe ™^, "^ "" """ ""■"«' "» "■"<»■»«■ ol 
 
 ..p»H.„dthe.ev;rh:i;rrirr°;;;r o'Ti:;^. ''»™- -' - 
 
 61. Deposit, »247.8B. Checks, «4.8B; «5.9(i| »10.00, »8 13 
 ^^62.^Deposit, ,307.63. Checks, ,142.15, ,16.85.. ,2.36, 
 
18 
 
 FIRST DEPARTMENT. 
 
 i 
 
 63. Depcsit, $429.21. Checks, $215.12; $32.98; $47.63; 
 $3.86 ; $2.25. 
 
 64. Deposit, $986.43. Checks, $314.18; $49.25; $57.62; 
 $39.84 ; $25.13. 
 
 65. Deposit, $276.20. Checks, $32.85; $24.19; $37.64; 
 $25.93 ; $3.27. 
 
 66. Deposit, $1000. Checks, $120.25 ; $14.98 ; $13.25 ; 
 $2.17; $25.00; $18.02; $27.38. 
 
 67. Deposit, $1254.86. Checks, $13.65 ; $92.80 ; $87.63 ; 
 $25.17 ; $264.86 ; $24.18 ; $37.20. 
 
 68. Deposit, $2765.90. Checks, $1249.84; $2.16; $3.95; 
 $276.48 ; $306.27 ; $14.27 ; $294.18. 
 
 69. Deposit, $2940.25. Checks, $140.00; $27.36; $69.80; 
 $1000.00; $297.60; $4.25; $324.18. 
 
 70. Deposit, $32956.25. Checks, $3425.84 ; $2625.18; $2.45; 
 $999.80; $243.60; $16.87; $1200.00. 
 
 EXERCISES FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 71. From 245 take 194. 
 
 72. From 376 take 216 ; then 84 from the remainder. 
 
 73. How old is a building in 1885 which was erected in 1734 i 
 
 74. How old is a man in 1886 who was born in 1784 '( 
 
 75. I give a ten-dollar bill in paying an account of $3.42. 
 How much change should I get ? 
 
 » 
 
 76. What number taken from 324 will leave 189 ? 
 
 77. The sum of two numbers is 524 ; the greater is 339 ; wht.t 
 is the less l 
 
 78. From the largest number that can be expressed by the 
 figures 2, 4, and 9, subtract 321. 
 
SUBTKACTION, 
 
 19 
 
 79. A school has 427 pupils, 139 of wh^mT^i^iT^. 
 many boys are tliere ? *^ °^ 
 
 WRITTEN DRILL EXERCISES. 
 81. I bought a cow for S35 and a horan f..r «ipk i ■ , 
 *12« down. How „,„„h have I y j to pa"? * ' ""' """' 
 
 .o?^hfrs^3:'';ss:'rd\^^^^^^^^^ -- ■-- - -e. 
 
 84. From 1005090010210 take 90091019012. 
 86. From 900999010908 take 78400215040. 
 
 86. Tlie sum of two numbers is snowni . +i, . . 
 
 what is tlie less ? ^^^ ' *^" ^'""^^^^ ^« 1^9082 ; 
 
 87. From the largest number thaf oar^ u^ , , 
 
 ^ ° "u'luer tnat can be expressed by the 
 
 r;:;:dV;h:itr«r '" -'-' -■'- -- 
 
 wide IS each leaf ? ^^^"- "^^o^ 
 
 90. How many days from March 16 until October 4 ? 
 
 t'>e 4 da.s Of October, and we C 2^ ll2r:^;:'ZT '"' ''''''''''' '^' 
 
 91. How many days from June 30 until December 26 ? ' 
 
 92. How many days from July 15 until February 22 ? 
 
 93. How many days from March 22 n,.f,n iv...^i.„_ .o . 
 
20 
 
 FIRST DEPARTMENT. 
 
 94. How many days from August 31, 1885, until June 1, 1880/ 
 
 95. The sum of three numbers is 101060 ; the first is 9999 ; 
 the second is 1010 more than the first ; what is the third number? 
 
 96. The sum of two numbers is 847 ; one is the dift'erence be- 
 tween 728 and 1110 ; find the other. 
 
 97. A man had ^425 in a bank ; he drew out ^149 ; deposited 
 $363, and then drew out $54. How much remained t(» his credit 
 in the ^ank ? 
 
 98. The difference between two numbers is 2001006 ; the 
 larger is 99009099 ; find the smaller. 
 
 99. Find the sum of the ages in 1887 of four men who were 
 born in 1813, 1792, 182G, and 183(> respectively. 
 
 100. Mr. Walker and Mr. Thompson live, respectively, 987 
 miles and 239 miles west of the same city. How far apart do 
 they live ? 
 
 III. MULTIPLICATION. 
 
 HINTS AND DEFINITIONS. 
 
 The product of two or more numbers is the result obtained by re);eatinff one 
 number as many times as there are units in the other. 
 
 MaltipUcation is the process of finding the pro<iuct of two numbers. 
 
 The multipUcaild is the number to be multiplied. 
 
 The multiplier is the number which shows how many times the multiplicand 
 is to be taken. 
 
 The sign Cf multiplication is x . it is read times, or multiplied by. 
 
 The product divided by the multiplicand gives the multiplier. 
 
 The product divided by the multiplier gives the multiplicand. 
 
 The multiplicand and multiplier are often called factors of the product. 
 
 The term COntinuod product is sometimes applied to the product of several 
 numbers. 
 
 The numerical result of multiplying one number by another is the same 
 whichever is taken as the multiplicand, the other being taken as the multiplier. 
 The product will always denote the same kind of units as the true multiplicand. 
 
MULTIPLICATION. 
 
 21 
 
 fference be- 
 
 SHORT METHODS. 
 
 < :arry when necessary. ^ * *"® 'eft-hand figure. 
 
 2 a^d TTf.T.V' "; r-'** ^"^ '"•^'*'"*"^ «*^- » = *»-- »v .. and 2 are 7 • 
 i ana 4, o , 4 and 8, 12. nut down *> unH >.»».. 1 . o j - ' ' 
 
 and carry 1 ; .5 and'., anS 1 are" 'then wH e th; ^t h -nd"; ' "V'' T' '^"" * 
 3942676. left-hrnd figure 3, and you have 
 
 101. 235x11. 
 
 102. 346x11. 
 
 103. 842x11. 
 
 104. 215x11. 
 106. 327x11. 
 
 106. 227x11. 
 
 107. 324x11. 
 
 108. 2135x11. 
 
 109. 4214x11. 
 
 110. 3132x11. 
 
 111. 2152x11. 
 
 112. 3728x11. 
 
 113. 2«>34xll. 
 
 114. 4215x11. 
 
 116. 23125x11. 
 
 116. 23412x11. 
 
 117. 13562x11. 
 
 118. 24234x11. 
 
 119. 31421x11. 
 
 120. 52123x11. 
 
 121. 21632x11. 
 
 h and place the product 24 in ,. •_'""'"P'{**'^ t'^" "^hthand Agures.eand 
 %ureH b'y the nL'bt next t; r 7 br8T7Ti aTdTh '"''' T ""' *'^ '^""'""'•^ 
 left Of the two fl,u..e. already obtained ^fk^ h "corrt t'Zr^ 'T "l ''' 
 pen or pencil, except to write the answer. ""ect result, 5624. Do not use 
 
 24 X 26, 4 X 6 -24, and 2 x 3 = 6, 624. 
 37x33, 7x3 = 21, and 3x4=12, 1221 
 91x99, 9x1=09, and 9x10 = 90, 9009. 
 
 122.24x20. 128.27x23. 134.128x122. 140 107x103 
 
 123.17x13. 129.18x12. 136.112x118. 141. IO8XIO2' 
 
 124. 34 X 36. 130. 33 X 37. 136. 104 x 106. 142 11 1 x 119 
 
 125.26x25. 131.42x48. 137.143x147. 143.132x138 
 
 126.35x35. 132.57x53. 138.152x158. 144.295x295 
 
 127.80x85. 133.61x69. 1.?ft io-t^^ioq ,.r ... „__ 
 
22 
 
 FIRST DEPARTMENT. 
 
 146. 04x90. 180. fi5xC.5, 154. 113x117. 168. 4!>7x493. 
 
 147. 37x33. 161. 84x8<). 166. 115x116. 169. 597x693. 
 
 148. 43x47. 162. 93x97. 166. 125x125. 160. 791x799. 
 
 149. 4(5;' 44. 163. 6Ux64. 167. 195x195. 161. 992x998. 
 
 NoTR.— Multiply 124 by 104. Multiply the excenses— that is, 24 by 4— and put 
 flown the profluct, 96, two pla<«H to the right-hand Bide, as In the illustration 
 below. Then add the two numbers, 104 and 124, omitting one of the me. at the 
 left. Carry when neoeggary. 
 
 124 24x4 = 96 
 
 104 4 + 4= 8 
 
 2+0= 2 
 
 12806 
 
 112 
 106 
 
 1 1872 
 
 NoTF.— Multiply 1234 by 1002. Multiply 234 by 2, and put down the product, 
 468, three places to the) right-hand side. Then add 2.34 and l'X)2. The product 
 will be 12.36468. 
 
 162. 112x106. 
 
 163. mxlOS. 
 
 164. 114x102. 
 166. 115x107. 
 
 166. 113x103. 
 
 167. 102x104. 
 
 168. 122x108. 
 
 169. 106x111. 
 
 170. 112x103. 
 
 171. 122x105. 
 
 172. 121x102. 
 
 173. 127x103. 
 
 174. 124x104. 
 176. 128x105. 
 
 176. 113x106. 
 
 177. 119x107. 
 
 178. 135x104. 
 
 179. 142x102. 
 
 180. 168x103. 
 
 181. 137x103. 
 
 182. 102x114. 
 
 183. 104x105. 
 
 184. 105x102 
 
 185. 105 :10<,. 
 
 186. 106x104. 
 
 187. 107x109. 
 
 188. 106x108. 
 
 189. 109x108. 
 
 190. 1007x1102. 
 
 191. 1312x1003. 
 
 192. 1009x1004. 
 
 193. 1003x1006. 
 
 194. 1007x1008. 
 
 195. 1012x1003. 
 
 196. 1012x1004. 
 
 197. 1098x1002. 
 
 198. 1006x1009. 
 
 199. Io02xl212. 
 
 200. 1342x1002. 
 
 201. 1099 X 1009. 
 
 202. 1199x1005. 
 
 203. 1265x1003. 
 
MULTIPLICATION. 
 
 23 
 
 the product, 
 The product 
 
 7 X 1102. 
 
 2 X 1003. 
 
 )xl004. 
 
 J X 1006. 
 
 7 X 1008. 
 
 2 X 1003. 
 
 2 X 1004. 
 
 ^ X 1002. 
 
 > X 1009. 
 
 i X 1212. 
 
 } X 1002. 
 
 ) X 1009. 
 
 > X 1005. 
 
 • X 1003. 
 
 N.,T«. -Multiply 96 by 97. Th. comjUement of * number i« the difference 
 between the m.u.ber and the unit .f the next h.Kher order. Th„«. the conX 
 nient of 96 i- 5 ; of 97 1» 3 ; of 9»7 In 13, etc. '^ 
 
 'MJ 5 (complement) 
 
 Q7 .3 (complement) 
 
 9215 
 
 Multiply the complements. Five times three are fifteen. Place 16 In the pro- 
 
 from the 96. There should be the sa„,e nun.ber of figures in the produc J in the 
 multiplier and multiplicand together. I'roautt as In tl»e 
 
 204. 97x98. 
 
 205. 99x88. 
 
 206. 99x97. 
 
 207. 97x90. 
 
 208. 96x98. 
 
 209. 99x96. 
 
 210. 96x95. 
 
 211. 97x95. 
 
 212. 95x98. 
 
 213. 99x95. 
 
 214. 95x94. 
 216. 94x96. 
 
 216. 9{)x94. 
 
 217. 94x98. 
 
 218. 95x9.3. 
 
 219. 96x93. 
 
 220. 93x97. 
 
 221. 98x93. 
 
 222. 97x94. 
 
 223. 94x93. 
 
 224. 93x92. 
 226. f)9x93. 
 
 226. 92x94. 
 
 227. 95x92. 
 
 228. 96x92. 
 
 229. 98x91. 
 
 230. 89x98. 
 
 231. 87x99. 
 
 232. 93x85*. 
 
 233. 92x92. 
 
 234. 994x995. 
 236. 993x994. 
 
 236. 99!) X 992. 
 
 237. 995x993. 
 
 238. 989x998. 
 
 239 9!;ix997. 
 
 240. 992x995. 
 
 241. 987x998. 
 
 242. 988x997. 
 
 243. 975x998. 
 
 NoTE.-Multiply 37 by 43. The n.ean number -that is, the number which Is .« 
 
 Ine I'ffh t' "'"'"■' "* ^' '^^ difference between the n.ean nun.ber and 
 
 one of the numbers, is 9. 1600 -9= 1591 = the product of 37 and 43. 
 
 244.87x73. 249.48x52. 264.112x108. 269.1012x988. 
 
 246.63x57. 260.24x16. 266.116x124. 260.1009x991 
 
 246.22x18. 261.31x29. 266.116x105. 261.1025x975. 
 
 247.93x87. 262.45x35. 267.118x122. 262.1004x996. 
 
 248.42x38. 263.72x68. 268.131x129. 263.1011x989. 
 
24 
 
 FIRST DEPARTMENT. 
 
 NOTK.— Multiply 76 by 46. Multiply units by unit» for the first figure of th»,' 
 product, the sum of the tens by units for the second figure, and tens by tens f„r 
 the third figure, carrying when necessary 
 
 76 
 46 
 
 3496 
 264. 56x56. 269. 99x49. 
 
 6x6 = 36, carry 3 
 
 6x(7 + 4) = 6xll=66, and 3 to carry, 69 
 
 4 X 7 = 28, and 6 to carry, 34 
 
 265. 72x32. 
 
 266. 94x44. 
 
 267. 65x75. 
 268.187 X 37. 
 
 270. 86 X 75. 
 
 271. 34 X 24. 
 
 272. 85x45. 
 
 273. 47x37. 
 
 274. 125x65. 
 
 275. 126x36. 
 
 276. 154x84. 
 
 277. 132x92. 
 
 278. 133x73. 
 
 279. 114x114. 
 
 280. 142x162. 
 
 281. 123x183. 
 
 282. 137 y 177. 
 
 283. 264x244. 
 
 NoTB.-Multiply 87 by 82. Multiply units by units for the first figure of the 
 product, the sum:of the units by tens for the second figure, and tens by tens for 
 the.reniaining figures, currying when necessary. 
 
 87 
 82 
 
 7134 
 
 7x2=14, carry 1 
 
 8x(7 + 2) = 8x9 = 72, and 1 to carry, 73 
 8 X 8 = 64, and 7 to carry, 71 
 
 284. 81 X 87. 
 
 285. 62x63. 
 
 286. 54x55. 
 
 287. 43 X 41. 
 
 288. 27 X 22. 
 
 289. 83x87. 
 
 290. 47 X 44. 
 
 291. 56x52. 
 
 292. 79 X 75. 
 
 293. 44 X 43. 
 
 294. 116x117. 
 
 295. 127x122. 
 
 296. 107x105. 
 
 297. 125x122. 
 
 298. 113x114. 
 
 299. 93x94. 
 
 300. 76x73. 
 
 301. 51 X 53. 
 
 302. 91x94. 
 
 303. 82x83. 
 
 NoTK. -Multiply 3-214 by 31 or 13. Instead of writing 31 under the multiplicand, 
 iis is tiie custom, multiply by 3 and place the product one figure to the le't, under 
 the multiplicand, and add. To multiply by 13, place the product one flgi; a to the 
 right and add. 
 
 3214 x 31 3214 x 13 
 9G42 9642 
 
 99634 41782 
 
 304. 2134 X 13. 306. 3242 x 15. 
 
 305. 1325x14. 307. 4135x16. 
 
 308. 2152x17. 
 
 309. 3428x18. 
 
MULTIPLICATION. 
 
 25 
 
 t figure of th(.' 
 ns by tens f^r 
 
 ; flffure of the 
 ns by tens for 
 
 multiplicand, 
 he le't, under 
 ? flgt e to the 
 
 310. 4006 X 19. 
 
 311. 8213x21. 
 
 312. 6204x31. 
 
 313. 3123x41. 
 
 314. 1242x51. 
 
 315. 2163x61. 
 
 316. 3216x71. 
 
 317. 2148x81. 
 
 318. 3123x91. 
 
 319. 4284 X 101. 
 
 320. 3121 X 102. 
 
 321. 4134 X 103. 
 
 322. 2162x104. 
 
 323. 1320x106. 
 
 324. 3121 X 106. 
 326. 4282x107. 
 
 BUSINESS EXERCISES. 
 
 326. 3109x108. 
 
 327. 1243x109. 
 
 328. 3152x201. 
 
 329. 4284x301. 
 
 330. 3212x401. 
 
 331. 4623x501. 
 
 332. 2136x601. 
 
 333. 1038x701. 
 
 eatS'S"''^'" **"' '°"°*'"'' '""■''''' ""** *'^ *«*^^ ^'-""^ »' ^^-^ articles under 
 
 334. Farm Produce. 
 
 213 lbs. butter at 22c. 
 102 lbs. cheese at 18c. 
 114 doz, eggs at 15c. 
 232 qts. milk at 6c. 
 127 bu. potatoes at efx-. 
 132 bu. carrots at 60c. 
 
 336. Farm Produce. 
 
 105 bu. turnips at 50c. 
 
 1 13 bu. beets at 80c. 
 
 114 bu. parsnips at 93c. 
 215 bu. onions at 9Sc. 
 236 bu. tomatoes at 42c. 
 137 doz. cabl)ages at 48c. 
 
 336. Farm Produces. 
 
 215 bbls. apples at $2. 15. 
 420 bu. plums at $1.20. 
 132 bu. peaches at $1.75. 
 215 bu. cherries at $1.35. 
 217 bu. pears at $1.50. 
 130 bu. quinces at $1.40. 
 
 337. Farm Produce. 
 
 113 bu. wheat at $1.22. 
 217 bu. barley at $1.05. 
 324 bu. oats at 4.5c. 
 716 bu. rye at 95c. 
 322 bu. peas at 75c. 
 136 bu. corn at S9c. 
 
 338. Grocerie.s. 
 
 25 lbs. rice at 4o. 
 
 37 lbs. tapioca at 15c 
 
 43 lbs. sago at 13c. 
 
 37 lbs. barley at 5c. 
 
 42 lbs. dried apples at 9c. 
 
 33 lbs. prunes at 7c. 
 
 339. Groceries. 
 
 25 lbs. sugar at 7c 
 32 lbs. tea at 47c. 
 84 lbs. coffee at ,52c. 
 62 lbs. raisins at lie. 
 39 lbs. currants at 9c. 
 4v iba. biscuits at I2c. 
 
26 
 
 FIRST DEPARTMENT. 
 
 NoTB.— Flour is sold at present by the barrel, bag, and sack. The barrel is sup- 
 posed to contain 106 pounds. The bag contains 100 pounds, and the sacks 50 
 pounds and 25 )>ound«. A stone is equal to 14 pounds. 
 
 340. Flour and Feed. 342. 
 
 2.5 bbls. flour at $ry.60. 
 32 bags flour at |2.75. 
 19 bags bran at 90o. 
 1 ) atone oat meal at 48c. 
 18 atone corn meal at 36c. 
 27 lbs. wheat meal at 7c. 
 
 341. Dry Goods. 343. 
 38 yds. cotton at 7c. 
 
 42 yds. cashmere at 58c. 
 37 yds. flannel at .'}5c. 
 52 yds. muslin at 19c. 
 64 yds. print. at 14c. 
 52 yds. lace at 98c. 
 
 Bltcherm' Supplies. 
 
 27 lbs. pork at 18c. 
 32 lbs. beef at 12c. 
 18 lbs. mutton at 14c. 
 12 lbs. veal at 15c. 
 18 lbs. lamb at 17c. 
 25 lbs. ham at 13c. 
 
 Coal and Wood. 
 
 12 tons hard coal at $6.25. 
 14 tons soft coal at .f4.35. 
 18 cords maple at .$6.50. 
 25 cords oak at $o SO. 
 12 cords pine at .f3.40. 
 24 tons coke at .$.3. tH). 
 
 i 
 
 EXERCISES FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 344. 2 X 3 X 5 s 4 X G X 10 X 2. 
 
 345. 4x2x5x7x2x3x10. 
 
 348. (9x2) + (7x2) + (12x2) + («4x2) + (8x2). 
 
 Note. — 9x2 plus 7x2 is eiiual to i) plus 7 or Iti multiplied by 2. In exercise 34(5 
 add 9, 7, 12, 24 and 8, and nuiltipl.\ the product by 2. 
 
 347. (12 X 13) + (8 x 13) + (87 X 20). 
 
 348. (24 X 32) + (23 X 32) + (47 x 28) + (53 x GO). 
 
 Note.— 24+23 = 47. 47x;»2 and 47x28-47x00. This and 53xOO = (47 + 53) or 
 100x60 = tK)00. Answer. 
 
 349. (321 X 224) + (247 x 613) + (753 x 381)) + (432 x 224). 
 
 350. (42x48) + (34x3G). 
 361. (55x55) + (43x47). 
 
 352. Finci the cost of 92 articles at 98 cents each. 
 
1RTLTIPLICATION, 
 
 ^ 
 
 n exercise 346 
 
 SO = (47 + 53) or 
 
 353. Find the cost of 83 articles at 87 cents each, 
 hourt ^""'^ '""'^ ""'" ^ ^""^ """"^ '"" ^^ ^'''"'' ""^ ^^ """*« ^" • 
 rC:^:.^L^, "-'"^'-^ ^^' - -^ ^'^ »«^"' ^He product to itse... 
 
 356. 2312 X 11. 366. 999 X 999. 357. 104 x 105. 
 
 WRITTEN DRILL EXERCISES. 
 368. Multiply 39005010 by 30900. 
 
 359. Find the product of 2005004 and 32605. 
 
 360. Find the product of all the numbers, of three figures 
 each, that can be expressed by the figures 3, 5, and 0. 
 
 .t^^;."""^,"'""^' '"""'^ ^"^ P*"^"^ ^''"^ ^*"^*"g 2352 loads of sand 
 at $1.25 per load? 
 
 362. How much will 753 pounds of sugar cost at 9 cents a 
 pound { 
 
 363. Find the cost of 122 building lots at $364 a lot. 
 
 364. A clerk's salary is $72 a month. If he spends $27 a 
 month, how much can he save in a year ? 
 
 365. What is the cost of 122 bales .>f cotton at 13 cents a 
 pound, If each bale contains 477 pounds ? 
 
 366. Mtiltiply 2 by 2, then 4 by 4, then that product by itself, 
 and m on until the product contains ten figures. 
 
 367. Find the cost of building 904 miles of railway at $2(5,342 
 a nule. ' 
 
 368. Multiply 20984(55 by 77, using factors. 
 
 369. Multiply 9800431 by (53, using factors. 
 
 370. Multiply the sum of 1001 and 10010 by their ditterence. 
 
 371. What will it cost to build 11 houses at $5329 each ? 
 
 buS'?^'"'^ *^'^ '''''^"^ ""^ ^^^^ ^"'''^^' of wheat at $1.13 a 
 
28 
 
 FIRST DEPARTMENT. 
 
 373. Find the value of 342 tons of hay at $17.25 a ton. 
 
 374. What is the ditference in cost of 174 head of cattle at 
 $37.75 a head and 1260 head of sheep at $5.50 a head ? 
 
 375. A miller exchanged 164 barrelb of flour at $7.35 a barrel 
 for 920 bushels of wheat at $2 a bushel, paying the balance in 
 money. How much money did he pay ? 
 
 376. Multiply 205090 by 106, using three factors. 
 Note.— Sound travels 1090 feet In one second. 
 
 377. You see the puff of a steam-whistle 11 seconds before 
 you hear the sound. How far are you from it ? 
 
 378. If a man travels 75 yards in a minute, how far will he 
 travel in 12 hours ? 
 
 IV. DIVISION. 
 
 HINTS AND DEFINITIONS. 
 
 The divisor is the number by which to divide. 
 
 The dividend is the number to be divided. 
 
 The result obtained by dividing is called the quotient. 
 
 The remainder is that part of the dividend which remains after the division 
 has been completed. 
 
 The Sign of division is -^ . it is read, divided by. 
 
 To prove the work, multiply the quotient and divisor, and add the remainder 
 to the product. 
 
 Any change in the divisor, by multiplication or division, will produce an oppo- 
 site change in the Quotient. 
 
 Any change in the dividend, by multiplication or division, will produce a similar 
 change in the quotient. 
 
 To multiply or divide both divisor and dividend by the same number does not 
 change the value of the quotient. 
 
 BUSINESS EXERCISES. 
 
 379. A bin containmg 237 bushels of wheat is sold for $272. 66. 
 How much a bushel is it sold for ? 
 
DIVISION. 
 
 29 
 
 r tlie division 
 
 toff** ^^ *^^ '' ^^'"^ ^*''' ^^ ^""' ""^ ^*^' ""^^^ '' *^^ P"^® P^^ 
 
 ^i; .Tn f '' "'*' ^"'*' P^"" P^""^ ^^^^" 1«0 P«"nd8 of mutton 
 cost ^14.40 ! 
 
 382. If 33 tons of coal cost |I206.25, what is the price of one 
 ton. ' 
 
 383. How many pounds of sugar can be bought for 8720 at 8 
 cents a pound ? 
 
 384. The cost of a piece of cloth was $112.70, and the price 
 «J.4o a yard. How many yards in the piece ? 
 
 386. A farm containing 167 acres was sold for $4474. 50. What 
 was the price per acre ? 
 
 386. How many cows, at $43 a head, will $19,606 buy ? 
 
 387. In a pile of 89,866 bridvH how many loads are there, eacli 
 load contaming 1248 bricks ? 
 
 388. A grocer paid $37.52 for 636 pounds of sugar How 
 nmch did he i)ay for each pound ? 
 
 389. When flour is worth $5.75 a barrel, how many barrels 
 can be bought for $1161.50 ? 
 
 whT If wV'?' ^' ^'''^'^ ^^1"^"^ --"g — Pe-ons, 
 what will be the share of each ? 
 
 391. A bookseller buys seven do^^en slates for $7.56 How 
 much does he pay for each slate ? 
 
 392. A fruit dealer buys 31 dozen oranges for $7.44 How 
 much does he pay for each orange ? 
 
 393. An exhibition is visited by 12,804 persons during six days 
 ..fa week. What is the average daily attendance ? 
 
 394. The weekly wages of 231 men is $1732.50. How much 
 a aay does each man receive ? 
 
 396. A merchant pays $7174 for 422 overcoats. At how much 
 each must he sell them to gain $1266 ? 
 
30 
 
 FrUST DEPARTMENT. 
 
 I 
 
 396. A butcher pays ^119.25 for 159 turkeys. At how much 
 a pair must he sell them to gain $39.75 ? 
 
 397. How many bales, each weighing 475 pounds, can be made 
 from 94,05*/ pounds of cotton ? 
 
 398. At $71 each, how many village lots can be bought for 
 $1,491,213? 
 
 WRITTEN DRILL EXERCISES. 
 
 399. Divide 20100120421 by 102003. Prove the correctness 
 of your answer. 
 
 400. The divisor is 2034 and the quotient 843. If the divisor 
 were 6102, what would the (juotient be ? 
 
 401. The divisor is 71421 and tlie quotient 403. If the divisor 
 were 10203, what would the quotient be ? 
 
 402. If the divisbr were 5 times as large, the quotient would 
 be 32701. What is the quotient ? 
 
 403. If the divisor were half what it is, the quotient would be 
 848. What is the quotient ? 
 
 404. When the dividend is 10824 the quotient is 12. If the 
 dividend were three times as large, what would the quotient be '! 
 
 405. The quotient is 30201. What would the quotient be if 
 both divisor and dividend were multiplied by 7 ? 
 
 406. The quotient is 0201. What would the quotient be if 
 both divisor and dividend were divided by 11 ? 
 
 407. How many barrels of flour can be bought for $2984 at $8 
 a barrel ? 
 
 408. Wiiat number multiplied by 12 will give the same pro- 
 duct as 1452 multiplied by 1001 ? 
 
 409. 2042005602-^103. Prove the work. 
 
 410. Divide 20563124 by 63, using factors. 
 
 411. What number must be taken from 204205 that it maybe 
 exactly divisible by 27 ? 
 
REVIEW. 
 
 31 
 
 412. How many busliels of oats at 5G cents a bushel can be 
 bought for $132.72? 
 
 413. Divide the product of 42160 and 10020 by the difference 
 between 109901 and 109889. 
 
 414. Divide 19094867 by 4009. Prove the work. 
 
 416. How many sevens must we add together to get 819 ? 
 
 416. The dividend is 74198, the quotient is 2005, and the 
 remainder is 24 less than the divisor. What is the divisor ? 
 
 417. Multiply 24004005 by 1155, and divide the product by 5 
 3, 7, and 11. I J , 
 
 418. If 35 be added to a certain number it will contain 53 
 13(J7 times. What is the number ? 
 
 V. REVIEW. 
 
 LOSS AND GAIN EXERCISES. 
 
 J-- 419. A man bought 225 acres of land at $15 an acre, and sold 
 the whole for $3125 ; how much did he gain or lose ? 
 
 NoTK.-The difference between the cost of anything and the price at which it is 
 sold 18 a gain or a loS8-a gain when the selling price is the greater, and a low 
 when the cost IS the greater. 
 
 L 420. Bought a farm for $2617, and sold it for $2199 • what 
 ' did I lose ? 
 
 ^ 421. Bought 246 barrels of flour at $5.50 a barrel, and sold 
 „; the whole for $1467 ; how much did I gain or lose ? 
 
 422. Bought 317 bushels of wheat for $421, and sold the whole 
 at 95 cents a bushel ; how much did I lose ? 
 
 423. Bought a farm of 155 acres, at $42.40 an acre, and sold 
 the same for $7195 ; what did I gain or lose ? 
 
 m. Bought a farm for $3695 ; spent $947 in improvements ; 
 sold out for $4267 ; how much did I lose ? 
 
32 
 
 FIRST DEPARTMENT. 
 
 Vi\ 
 
 426. A farmer bought 30 cows for $540 ; he fed them for one 
 year at a casli expense of $7.60 per head ; he then sold the entire 
 herd for 0870 ; how much did he gain or lose ? 
 
 426. Bought a house and lot for $2127 ; built an addition to 
 the house at an expense of #365 ; sold out for 82598 ; how much 
 did I gain or lose ? 
 
 427. Bought a fishing boat for $195 ; spent K35 for painting 
 and repairs ; received $42 for the use of the boat ; sold out for 
 $212 ; how much did I gain ? 
 
 428. A newsboy buys 144 newspapers each day at 20 cents a 
 dozen. He sells them at 3 cents each. At the end of the week 
 he has 18 old papers on hand. How much money has he made 
 during the week ? 
 
 429. A man rented a skating rink for three weeks at $95 a 
 week. His expenses for heat and light were $1.75 a day for 18 
 days. He charged 25 cents for adults, and 15 cents for children. 
 The total attendance of the former was 3254, and of the latter 
 2106. How much did he gain ? 
 
 430. A merchant bought 120 overcoats at $15.85 each. He 
 sold half of them at $25 each, and the others he sold in a job lot 
 for $820. How much did he gain or lose ? 
 
 431. A book agent bought 90 books at $2.75 each. He sold 
 them at $5 each. His expenses were $12. 25. He was unabl'^ to 
 collect for three books. How much did he gain or lose ? 
 
 432. A fruit dealer buys 242 dozen oranges at 13 cents a dozen ; 
 104 oranges are spoiled ; he sells the others at the rate of 14 for 
 25 cents. H ^w much does he gain ? 
 
 433. A farmer bought a ten-acre field of ripe wheat for $175. 
 He paid $1.35 an acre for cutting a I saving, 3 cents a bushel 
 for thrashing and cleaning, and $2 a load (42 bushels) for team- 
 ing. The wheat yielded 21 bushels to the acre, and was sold for 
 $1.35 a bushel. How much did the farmer (tain or lose ? 
 
REVIEW. 
 
 83 
 
 MISCELLANEOUS EXERCISES. 
 434. Find tlie sum of all the numbers between 897 and 904 
 
 ;^n^:,!:!!!.^!r^^^-f-.-'^-.W'« number is 
 
 What number haa 
 
 13 when the class numbers from the right 
 he when they number from the left ? 
 
 436. Divide 26050432105 by 132, using factors. 
 
 437. A steamboat can run 10 miles an hour down a river, and 
 8 miles an hour up. After running down the river for 24 hours 
 how long will she be in returning ? ' 
 
 438 If 49 be added 101 times to itself, by how much will the 
 result fall short of 5000 ? 
 
 98^2?^'"'' "^""^ *'"""' ™"'^ ^^^ ^' *^^'^ *" ^22 to make 
 div1!fbleT;i20T'" ""^' '^ "^'^^ *^ ''^^ '^ "^'^^^ '' --«y 
 
 it «tirib;:t r58t '' "'*^^^'^' ^^^-^ '''''' *^ ™^^^ 
 
 lea^in '''' ""^""^ *'"'^' "*'"'* ^^ ^^ subtracted from 600455 to 
 
 ^.^L^^ ^7 ^T ^''""'"" *" ^"^'^•^^^' ** 3 cents a mile, 
 was ^11 55. I returned by boat at one cent less a mile. What 
 was my fare for the round trip ? 
 
 m. By what number must 14212 be divided so that the result 
 may be as much above 692 as it is beh w 804 ? 
 
 from k l\ f ^' '"^^^^ .*" f '''*^^" """^^"'*' ^^ "»^y ^« subtracted 
 tiom It 91 tmies. Fmd the number. 
 
 446. I have a coin, and on it is stamped MDCIV. In what 
 year was it made ? f . xn wnat 
 
 447. A boy drives the cows twice a day to be milked • how 
 
f 
 
 i 
 i 
 
 u 
 
 34 
 
 FIRST DEPAUTMENT. 
 
 448. I bought 7 cows at $37 each. At how much a head muBt 
 ^ I sell them to gain $36 ? 
 
 449. What is the largest number that can bo taken 314 times 
 from the product of 8(i52 and 37 so as to leave a remainder of 
 29280(} ? 
 
 460. How long a string will it take to go round a house 42 
 feet long and 36 feet wide ? 
 
 451. Find the sum of all the numbers ending with 8 or 1> 
 between 700 imd 800. 
 
 462. Find the number which subtracted from 900000 leaves 
 751930. 
 
 463. Multiply the sum of 80297 and 40025 by the difference 
 between 789 and 094. 
 
 464. A drover bjought 84 head of cattle at $21 each, and sold 
 _J''^them at $28 each ; how much did he gain ? 
 
 , 486. Midtiply 2010500401 by 30102. 
 
 466. When 11 has been added 19 times to a certain number 
 the result is 33 less than 12 times the original number. What 
 is the original number ? 
 
 457. When 300 is added to a certain number the result is 75 
 more than 4 times the number. Find the number. 
 
 458. Which is the nearer number to 100010 : 200009 or 11 ? 
 
 469. Bought 45 head of cattle at $24 each, and paid $600 cash, 
 and the remainder in sheep at $4 a head ; how many sheep were 
 required to balance the debt ? 
 
 460. A man paid $3750 for some village property, which was 
 $1243 less than he paid for a farm ; what did he pay for both ? 
 
 461. Find the sum of the five largest numbers that can be 
 expressed by the figures 9, 8, 0, 4, and 2. 
 
 462. A mechanic earns $90 a month ; his expenses are $784 a 
 y^ year ; hov/ l^mg will it take him to save enough to buy a house 
 
 worth $2960 ? 
 
 11 fi 
 
 M 
 
REVIEW. 
 
 a, head munt 
 
 85 
 
 result is 75 
 
 that can be 
 
 463. A farmer's wife sokl a grocer 16 dozen eggs at 14 cents 
 and 27 pounds of but^.r at 22 cents ; she receive^Tn payment 12 
 pounds of sugar at 11 cencs, and cash for the balance. How 
 n»uch cash did she get i 
 
 for «11.25; ..r the apples he paid 2 cents each, and for the 
 oranges 3 cents eacli ; how many of each did he buy ? 
 
 466. Two men start from the same place and travel in opposite 
 ttetr; one at the rate of 3 miles an hour and th. otW a 
 the mte of 4 miles an hour ; how far apart will they be in 240 
 
 .33. I bought a house for |4600 ; spent «1263 in in.prove- 
 .nents, and then sold it for ^16226 ; how much did I gain? 
 
 467. Jf any number be doubled, the result increased by 1 
 the .sunx multiphed by 3, the product diminished by 9, and the 
 remamder div.ded by 6, the quotient will be less by unity than 
 the number taken at first. Why v ""y tnan 
 
 7f Q9?' ^7 T""^ ^"'''' "'^^ *^' difference between 2184 and 
 7W2 be taken from 8 times the sum of 56213 and 49439 so as to 
 leave a remainder of 24524 ? »«> t., 
 
 469. The divisor is G3875, the quotient 46938, and the re- 
 .namder the largest whole number possible. Find the dividend. 
 
 470. A railway charges a cent a mile for the first fifty miles 
 or carrying a cord of wood, and then 3 cents for every 4 miles 
 
 beyond the fifty. What will it cost to cany 250 cords^O miles" 
 
 471. Find the diflerence between the sum ot 73927 and 8496 
 .ind the product of 1987 and 39. 
 
 472. Of what number is 7589 both divisor and quotient ? 
 
 473. A farmer has an orchard containing 580 trees • each tree 
 
 «m x::r -' ■""*' ' ''°" ■"""" -- "^^ appie',:r :: 
 
 en^n^T'T' """,'""■ f'^'^ '° *''" """' °* "" ">« numbers M,.t 
 - . .wt„cen 1 aim ±ou win make a million ? 
 
36 
 
 FIRST DEPARTMENT. 
 
 q m 
 
 11 
 
 475. I bought 28 poiiiulH of rice at \) cents, 12 |H>un(l8 of sugar 
 at 11 cents, 4 i>ouu(ls of tea at 75 cents, and three lemons at 3 
 cents eajh. Wliat change should I receive if I give a ten-'l«»llar 
 bill in paying 1 
 
 478. If a clerk receives 8<>40 a year, and his expenses are $326 
 a year, how niany years will it take him to pay for a 5H-acre farm 
 at 646 an aero ( 
 
 477. In how many days will a clock strike 2G52 strokes < 
 
 478. A laborer receives #22 a month and board f(»i" 8 months 
 of the year ; the rest of the year he is idle and pays $14 a month 
 for "board ; allowing him $36 a year for other expenses, how 
 much should he save in 3 years i 
 
 479. A merchant bought 2(5 pieces of broadcloth, each con- 
 taining 63 yards, at )$4 a yard ; how much did the whole cos*- 
 him 'i 
 
 480. Divide 318493428 by 8607. 
 
 481. Two persons start from the same point to travel in oppo- 
 site directions ; one travels 20 miles a day, and the other 35 
 miles a day ; how far apart will they be at the end of 46 days ? 
 
 482. What number must be :lded 29 times to 466 to make 
 the sum equal to 1799 ? 
 
 483. What number must be taken 38 times from the sum of 
 864, 923 and 638 to leave 297 ? 
 
 484. The product of two numbers is 688 ; one of the numbers 
 is 12 times the other. What are they ? 
 
 485. A farmer traded two old stoves, weighing together 672 
 pounds, for a new stove worth $27.60 ; the stove dealer allowed 
 him 3 cents a pound for the old stoves ; how much cash should 
 the farmer pay ? 
 
 486. A postman called at every second house on a street ; at 
 half the houses at which he called he delivered 2 letters, and at 
 the other half, one letter each ; he delivered in all 360 letters. 
 JT/'jw inanv boup.ep, on the fttreet ^ 
 
 % 
 
REVIEW. 
 
 37 
 
 ten-'loUar 
 
 he sum of 
 
 e numbers 
 
 487. The dividend in 2547340, the (luotient 254, the remainder 
 2054 lesB than the divisor. Find the divisor. 
 
 488. A man bought on speculation 08 horses at $84 each ; 11 
 of them die ; at how much each must he sell the others to gain 
 
 v444 I 
 
 489. What is the sum of the ages in I88(i of four persons who 
 were bom in 1775, 179C, 1810 and 1832 { 
 
 490. One train left Chicago at 3 p.m. at 28 miles an hour ; a 
 second train left at 6 p.m. nt 30 miles an hour ; when will the 
 fast overtake the slow, and how far from Chicago ? 
 
 491. It is found that if 593 be subtracted 347 times from a 
 certain n- mber the remainder is 287. Find the certain number. 
 
 492. Find the number .such that if it be added 66 times to 
 29483 the sum will be 238027. 
 
 493. A carpenter earned ^03 by working a certain number of 
 days ; it he had worked 13 days more he would have earned 
 ^102. Find his daily wages. 
 
 494. A farmer has 834 trees in two orchards he has 142 more 
 in one than in the other. How many has he in each ? 
 
 495. A house and lot cost $8358 ; the house cost times as 
 much as the lot. Find tlie cost of each. 
 
 496. If a sheep gives 8 pounds of wool in a year, how many 
 p.nuiu8 can be got from 30 sheep in 4 ye.rs, and what will it be 
 worth at 38 cents a pound ? 
 
 497. In a certain school library there are 879 books, which 
 number gives 29 books to «ach pupil and 9 books over. How 
 many pupils are there ? 
 
 498. The sum of two numbers is 3785, and the greater is 249 
 more than the less. What are the numbers ? 
 
 499. At an election A and B were the only candidates ; the 
 whole vote cast was 6235 ; A was elected by a n^ajority of 647. 
 
 ■ — — -^ »• '^t/t^o tiiii xj nvh ; 
 
■S^*t-»'iJ-yA'ilS*^-f*:)i 
 
 38 
 
 FIRST J)EPARTMENT. 
 
 / 
 
 500. The sum of two numbers is 4628 ; their difference is 228. 
 What are the numbers ? 
 
 601. By what must you divide the sum of the digits to 
 I ibtain 5 ? 
 
 502. What is the nearest number to .34792 that can be divided 
 by 29(5 without a remainder '( 
 
 503. George Wilson has made 7072 chairs in 4 years, making 
 each year 150 more than the preceding year. How many did he 
 make each year ? 
 
 504. How much water must be added to 90 gallons of wine- 
 worth $4t a gallon so that the mixture may be worth $3 a gallon ? 
 
 505. A man spent S160 for a horse, which was ^110 less than 
 three times as much as he paid for his buggy ; and his buggy 
 cost $fi more than 4 timfes the price of the harness. How much 
 did the harness cost ? 
 
 506. When 402 is taken from a certain number, and the 
 remainder is divided by 5, the quotient obtained is 42021. What 
 is the number '. 
 
 507. A ton of coal lasts a family 14 days; if coal is worth 
 $5.25 a ton, what will their coal cos! from October 1, 1885, till 
 March 31, 188(), inclusive ? 
 
 508. Whfit is the difference in value between 620 cords of 
 wood at $3.47 a cord, and 620 tons of coal at $4,65 a ton ? 
 
 509. A purse contains ten-dollar bills, five-dollar bills, and 
 one-dollar bills, an equal number of each; when the tens are 
 taken out $42 remains ; when the fives are taken out $77 remains ; 
 and when the ones are taken out $105 remains. How many bills 
 of each kind does the purse contain ? 
 
 510. You find an old book with the date MDCXLVII. printed 
 at the bottom of the title page. In what year was it published ? 
 
 511. A grocer bought 15 tubs of butter, each containing 48 
 pounds, at 28 cents a pound, and sold the same at 35 cents a 
 pound. What was his gain ? 
 
REVIEW. 
 
 39 
 
 612. A produce dealer bought 1488 bags of potatoes at $1 
 a bag, and sold them at $1.57 a bag. What did 1 
 
 22 
 
 gain 
 
 fJ^^^^^Z '"T ,^""'' "' «"cce88iun can 3589 be subtracted 
 from 241462, and what will be the final remainder ? 
 
 514. What number added to 909900190 makes 3000000201 ? 
 
 ^^^; ^ ""'I't^''' ^'''"^'^ ^'^^' ^" ^''^ y^'^rs ; he gained the 
 second year $1053 more than the first. What was his gain each 
 
 516 How many pounds of tea at 78 cents a p(.und must be 
 given for 375 bushels of wheat at $1.56 a bushel ? 
 
 617. What number must be taken from 20010032 so that it 
 may be exactly divisible by 909 ! 
 
 618. What number besides 137 will exactly divide 11371 ? 
 
 619. The President of the United States receives $50,000 a 
 aXy > '"'''''"'^ ^^ '"'*'' '' ^'''''' ^'""^ '""''^ ^""^^ ^'^ r«««ive 
 
 520. How many times can 1440 be subtracted from 82354(50800 ! 
 
 621. When 9 is added to the dividend the quotient is 39 and 
 when 2 IS subtn.cted from the dividend the quotient is 38 
 What 13 the dividend ? 
 
 622. The quotient is 6 times the remainder. The divisor is 7 
 times the quotient. Find the dividend, the remainder being 45 
 
 .ZZl-flTj"' ''''''-' '''''' ''' -"" "' ''^ — -"^e. b. the 
 
 A 32f!nd!i"'^ *''' ''''''''^' "^ ^''^' *'^^' ^^^' ^^' *^' ^^^' 2^^^' ^28, 
 
 $i^, f^^3r^^^^ '' '''-''^ «*^' ^^^•^^' *i««o, 
 
 625. What is the smallest number divisible by 7 which added 
 to 3264 makes the sum divisible by 12 ? 
 
 626. The aggregate attendance at a public school during 167 
 days was 31,557. What was the average daily attendance f 
 
r 
 
 40 
 
 FIRST DEPARTMENT. 
 
 I 
 
 527. A merchant mixes 1 pound of tea worth 50 cents with 3 
 pounds worth 70 cents. What will a pound of the mixture be 
 worth '( 
 
 528. A farmer mixes 12 bushels of oats worth 35 cents with 
 13 bushels of barley worth (iO cents. What is a bushel of the 
 mixture worth ? 
 
 529. A grocer mixes 15 pounds of coffee worth 27 cents, 3 
 pounds worth 35 cents, and 3 pounds worth 40 cents. What is 
 a pound of the mixture worth ? 
 
 530. A merchant's cash receipts for a week are $231.14, 
 $125. G3, li;()32.H4, $321.15, $424.17, and $5G3.85. Find his daily 
 average. 
 
 531. When 179 is added to the dividei d the quotient is 237, 
 and when 253 is subtracted from the dividend the quotient is 
 233. What is the divisor ? 
 
 532. For each dollar bill that I have, I have five silver half- 
 dollars ; and for each silver half-dollar that 1 have, I have 27 five- 
 cent pieces. I have $51.25 in all How many live-ceixt pieces 
 have 1 ? 
 
 533. Find a number to which if 369 be added the sum will be 
 1001 less than 9090. 
 
 534. If 54 clerks i-eceive $7770 for 16 weeks' work, how much 
 a day does each receive ? 
 
 535. Two men had $7583 divided between them ; the dittereuce 
 between their shares was $223. What did each get ? 
 
 536. A has 11 times and C 25 times as much money as B. 
 The difference between A's money and C's money is $472.50. 
 How much money has B ? 
 
 537. A farmer's horses, cattle and sheep together numbeir 96. 
 He has three times as many cattle as horses, and 4 times as many 
 sheep as cattle. How many of each has he ? 
 
 ^ « 
 
SECOND DEPARTMENT. 
 
 I. FACTORS AND MULTIPLES. 
 
 HINTS AND DEFINITIONS. 
 \C An Integer U a number that represents whole things. 
 An even number is a number exactly divisible by 2. 
 An odd number is a number not exactly divisible by 2 
 
 Thu^^r°r;hV^.^::;;v.\^:"^^^^^^ 
 
 factors of 06. ' of 6 . 5 and 7 are the factors of 35 ; 3, 2, and 11 are the 
 
 3. t rZ^T^r-^Z:^ -'-'^ ^^ -^y ^-f and 0,.. Thus 
 
 its;if:r!r' ^"""^^ ' ^ "-•''^^ ^^-^^ •^^ «*»'- '-^^^ or divlso. than 
 A prime factor is any prime number used as bl factor 
 
 ..Id 72. ™»'»""- Thu, ,. « „„„„<,„ ,„i„, „, J, ^„^ ^ ^^ ^j ^ 
 
 A common multiple of two or more numbers is a„v ,.n.,.h .u . • 
 divisible bv each of then.. Thus 20 is a eonnn: muUMl'ou'l^V ^ " ""^*'^' 
 
 The least common multiple of two or more number, wth« I * 
 is exactly divisible by each of them. ''"mbeis is the least number that 
 
 Any number is divisible by a if the sum of its dijfits is divisible by 3 
 
 Any number is divisible by 4 if it end with two or more ciphers or if tv.» 
 expressed by its two right-hand flgur, . be divisible by 4 '^"' 
 
 Any number is divisible by .5 if its right-hand figure be 5 or 0. 
 
 Any number is divisible by 9 if the sum of its digits be divisible by 9. 
 
 Any number is exactly divisible by 7, 11. and IS if fho ... •. . 
 thousands' period are the same. ' ^' """' P^"*^ ''"^ t^e 
 
 The product of all the prime factors of a number is equal to that number 
 
 numbe A'^^t U*'.?"'"'"* T"^" """"■■' *"' '"''' '••"'"»«" "^"'"»'« "' two 
 numners is rqual to the proauct or cne two numbers. * " 
 
(! 
 
 NiiiiiwaiMiwiiiiiiiMiMiiABiBii 
 
 42 
 
 SE(JOND DEPARTMENT. 
 
 EXERCISES FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 1. Find thu sum of the even numbers between 1 and 15. 
 
 2. Find tlie sum of the odd numbers between 2 and 14. 
 
 3. Find the sum of all the prime factors of 210. 
 
 4. Name the prime numbers from 1 to 30. 
 
 5. Name the largest prime immber expressed by two figures. 
 
 6. Name the smallest prime number expressed by three 
 hgures. 
 
 7. Find the sum of the six smallest prime numbers. 
 
 8. Find the sum of the seven smallest composite numbers. 
 
 9. What is the highest common factor of 21, 28, and 35 ? 
 10. What is the least common multiple of 3, 5, and 7 ? 
 
 WRITTEN DRILL EXERCISES. 
 
 11. What are the prime factors of 390 ? 495 ? 968 ^ 
 
 12. What are the prime factors of 756 ? 1089 ? 8004 ? 
 
 13. What are the p»ime factors of 1728 ? 1 5465 ? 3003 ? 
 
 14. What are the prime factors of 4158 ? 3150 ? 2310 ? 
 
 15. What are the prime factors of 0552 ? 7826 ? 5368 ? 
 
 16. What are the prime factors of 5075 ? 9576 ? 1165 ? 
 
 17. What is the sum of the prime factors of 34650? 
 
 18. What is the sum of the prime factors of 172800 ? 
 
 19. Find the prime factors common to 144 and 180. 
 
 20. Find the prime factors common to 462 and 440. 
 
 21. Find the prime factors common to 168, 256, and 320. 
 
 22. Find the prime factors common to 326, 540, and 635. 
 
FACTOHS AND MULTU>LES. 
 
 43 
 
 res. 
 iree 
 
 23. What is the largest prime factor common to 1561 and 1477 ? 
 
 24. What is the largest prime factor common to .385 and 735 ? 
 26. What is the greatest common divisor of 272 and 425 ? 
 
 26. What is the greatest common divisor of .394 and 672 ? 
 
 27. What is the greatest commcn divisor of 825 and 060? 
 
 28. What is the greatest common divisor of 2121 and 1313 ? 
 
 29. What is the greatest common divisor of 348, 609, and 580 ? 
 
 30. What is the largest multiple of 3 and 5 that can be ex- 
 pressed by three figures ? 
 
 31. What is the smallest multiple of 2 and 7 that can be ex- 
 pressed by three figures ? ' "« ex 
 
 32. What is the largest multiple of 5 and 7 that can be ex- 
 pressed by four figures ? 
 
 33. What is the smallest multiple of 2, 3, and 5 that can be 
 expressed by three fig- - - r 
 
 nr^' ^u'll" ^^1 ^^' - "' ^^*'P^^ ''^ ^' ^' ^^d 7 that can be ex- 
 pressed by three figur. ' 
 
 36. AVhat is the least number of which 2, 3, and 5 are factors ? 
 36. What is the least number of which 3, 5, and 7 are factors ? 
 
 factorsT^""^ '" *^^ ^^^' """'^^' ""^ '^^'''^ ^' ^' ^' •'^""^ ^ *^« 
 
 fac^tors^'^* '' *''' ^^^^ ''""'^*'' °^ ""^^^^ '^' *' "^' ^' ''''^ « ^^« 
 
 39. Find the least common multiple of 3, 5, 6, 7, and 8. 
 
 40. Find the least common multiple of 4, 5, 9, 12, 15, and 20. 
 
 41. Find the least common multiple of 10, 16, 24, 40, and 64. 
 
 42. Find the least number which, divided by 3, 7, 11 or 13 
 will give a remainder of 2 in each case. 
 
 43. Find the greatest number that will divide 748 and 927 
 and give the remainders 13 and 17 r««n«..fj,,.iv 
 
44 
 
 SECOND DEPARTMENT. 
 
 -/ 
 
 44. Find the sum of all the prime numbers between 10 and 
 100. 
 
 46. What is the smallest prime number that can be expressed 
 by four figures ? 
 
 Note.— L. C. M. stands for "least common multiple," and H. C. F. for "highest 
 common factor." 
 
 46. The L. C. M. of 391 another number is 12121, and the 
 H. C. F. is 23. What is the other number ? 
 
 47. The product of the H. C. F. and L. C. M. of two numbers 
 ^^ is 1728 ; one of the numbers is 90. Find the other, 
 
 48. The sum of two numbers is 650 ; their common factor is 
 11 ; the ditference between the other two factors is ' 2. What 
 are the numbers ? 
 
 49. The sum of two nui >.bers is 680 ; their common factor is 
 7; the difference between the other two factors is 10. What 
 are the numbers ? 
 
 II. COMMON FRACTIONS. 
 
 HINTS AND DEFINITIONS. 
 
 A fraction ia one or more of the equal parts of a unit. 
 
 A fraction Is usually expressed by two numbers, one written above the other, 
 with a line between. 
 
 The denomlJiatOr of a fraction is the number written below the line, and shows 
 the number of equal parts into which the unit is divided. 
 
 The numerator of a fraction is the number written above the line, and shows 
 Iiow many of the equal parts are used. 
 
 A mixed number is a whole number and a fraction united. 
 
 Multiplying the numerator, or dividing the denominator, multiplies the value of 
 a fraction. 
 
 Dividing the numerator, or multiplying the lenomlnator, divides ttae value of 
 a fraction. 
 
 Multiplying or dividing both terms by the same number does not change the 
 value of a fraction. 
 
COMMON FRACTIONS. 
 
 45 
 
 ESBRCISBS FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 60. In 3 fourths how many sixteenths ? 
 
 61. One third of a year is how many sixths of a year ? 
 
 62. Two thirds of a mile are how many ninths of a mile ? 
 
 53. Four fifths of a month are how many fifteenths of a month ? 
 ^ j 54. Express three of the seven equal parts of a unit. 
 J 55. Express seven of tlie twelve equal parts of a unit. 
 ^j 66. How many thirds in 5 ? 
 / 67. In 18 units how many fourths ? 
 /| 58. Reduce | to a fraction whose denominator is 32. 
 
 , 59. Change ^^ to an equivalent fraction having GO for its de- 
 '"^1 nominator. 
 
 WRITTEN DRILL EXERCISES. 
 
 Direction. -The twenty-five fractions which follo^^ are to be 
 lowest terms. 
 
 reduced to their 
 
 
 60. 
 61. 
 62. 
 68. 
 
 64. M. 
 
 3 
 V- 
 
 10 
 T2- 
 
 12 
 
 65. 
 66. 
 67. 
 68. 
 69. 
 
 If. 
 
 ft 3 
 24 
 
 28 
 
 70. 
 
 71. 
 72. 
 73. 
 
 it. j-g 
 
 fl4 
 
 84 
 
 a a 
 'ST- 
 
 75. 
 76. 
 77. 
 78. 
 79. n 
 
 2V' 
 
 H. 
 
 to 
 
 48 
 ff¥- 
 
 27 
 
 80. t' 2 
 81. 
 
 82. 
 
 8 5 
 T(J5- 
 
 90 
 
 83. AV 
 
 06 
 
 Direction. -The twenty-five mixed numbers which follow are 
 fractional form, with numerator and denominator only. 
 
 84. 
 
 to be reduced to 
 
 85. 27^ 
 
 86. 32J. 
 
 87. 43i. 
 
 88. m. 
 
 89. 16*. 
 
 90. 13|. 
 
 91. 29J. 
 
 92. 40J. 
 
 93. 82^. 
 
 94. 63.V. 
 
 95. 3f. 
 
 96. "":. 
 
 97. 4f . 
 
 98. 5|. 
 flQ as. 
 
 100. 4|. 
 
 101. 6J. 
 
 102. 7^. 
 
 103. 8f 
 
 lA/l 
 
 105. 
 106. 
 
 >7 3 
 'ITT' 
 
 M 4 
 
 05 
 
 107. 5/^. 
 
 108. 6tAj. 
 
 1 /VQ Ck T 
 
SECOND DEPARTMENT. 
 
 DlRBCTIOM 
 
 numbers. 
 
 110. V 
 
 111. V 
 
 112. V 
 
 113. ^ 
 
 114. ^f 
 116. ^ 
 116. ^} 
 
 -The thirty-five fractiontt which follow are to be reduced to mixed 
 
 117. ^ 
 
 118. n 
 
 119. V 
 
 120. ^ 
 
 121. {\ 
 
 122. H 
 
 123. V 
 
 124. -4^. 
 126. H^- 
 
 126. H^. 
 
 127. ^. 
 
 128. H^. 
 
 129. W 
 
 130. W 
 
 131. H^ 
 
 132. ^;^a 
 
 133. W 
 
 134. W 
 136. ^ 
 
 136. H^ 
 
 137. Ap 
 
 138. ^^ 
 
 139. ^^ 
 
 140. ^^^ 
 
 141. H^. 
 
 142. ^^ 
 
 143. ^4f^. 
 
 144. ^e^ 
 
 No'iE.— In order that fractions may be added they must have like denominators 
 and be parts of like units. 
 
 145. h + \. 
 
 156. Hf 
 
 165. 
 
 i + i 
 
 176. 
 
 f + f 
 
 146. i + i 
 
 156. i + i 
 
 166. 
 
 h + l 
 
 176. 
 
 f + f 
 
 147. i + i 
 
 167. i + f 
 
 167. 
 
 l + f 
 
 177. 
 
 f + ^- 
 
 148. h + h 
 
 168. i + i 
 
 168. 
 
 f+i 
 
 17C. 
 
 f+A- 
 
 149. ^+f 
 
 169. l + \. 
 
 169. 
 
 f+f 
 
 179. 
 
 f + rV 
 
 150. i + i 
 
 160. Hi- 
 
 170. 
 
 i + f. 
 
 180. 
 
 ^ + A- 
 
 151. ^+i 
 
 161. ^ + tV 
 
 171. 
 
 Hf 
 
 181. 
 
 T^ + A 
 
 152. i + i 
 
 162. * + iV 
 
 172. 
 
 l + i 
 
 182. 
 
 T^ + l- 
 
 153. i + i. 
 
 163. i + :A^. 
 
 173. 
 
 *+!• 
 
 183. 
 
 TAr + f 
 
 154. i + i 
 
 164. HA- 
 
 174. 
 
 f+f- 
 
 184. 
 
 t\ + M- 
 
 NoTB.— The small figures to the right of the numbers below represent fourths. 
 Thus 482 = 48J or 48^. This method of writing small fractions is frequently made 
 use of by business men. 
 
 185. Add 242, 25, 261, 273, 29^, 28^, 24, 23^, 27^ and 29". 
 
 186. Add 293, 222, 273, 292, 22s, 213, 263, 281, 25^, and 323. 
 
 187. Add 492, 542, 482, 472^ 563^ 518^ 52, 43, 472, and 46i. 
 
 188. Add 73' 722, 733^ 743, 752, 7C3, 771^ 722, 732^ and 742. 
 
 189. Add G41, 022, (53^ ^42, 653, q2\ 662, 643, q2\ and 632. 
 
COMMON FRACTIONS. 
 
 47 
 
 ».RKrT,o.v.-rn addinK the frat^tions in the flnt column below add tha fln.t *^ 
 'racfons, Vhen add their .um and the thini fraction. Do uTZ'e ^n Tp^Zil 
 
 190. h + }+h- 
 
 191. i + i + VV- 
 
 192. ji + i + ^. 
 
 193. i+i + U' 
 
 195. l+f + H. 
 
 196. l+f +H. 
 
 197. l+f+i^. 
 
 198. ^ + HH. 
 
 199. l + f + ^V 
 
 200. f + HijV 
 
 201. f + f + f|. 
 
 202. ^ + A + I|. 
 
 203. l + f + A- 
 
 204. /ir + TV + TV.- 
 
 206. Hi + i + i + i + f + f 
 
 206. ^ + i + f + i + j + | + |. 
 
 207. i + l + i + f + l + i + J. 
 
 208. J + Hf + | + | + f + j. 
 
 209. Hi + * + i + |. + Hii«iT. 
 
 210. Hf + | + f + j + j + ^. 
 
 211. l + i + | + | + | + 6 + ^^_ 
 
 212. t + § + f + | + i + i + ^. 
 
 213. i + i + | + H* + A + TV 
 
 214. f + Hi + i + HT^ + /^. 
 216. * + ^ + f + i + ^ + ,a^ + ^. 
 
 216. S + ^ + l + i + f + TAy + H. 
 
 217. ^ + f + f + i + ,^ + /^ + ^. 
 
 218. § + f + l + | + rV + M + i^. 
 
 219. l + f + i + HH + iJ + H. 
 
 NoTE.-In adding mixed numbers add the fractions first ami t^ th ■ 
 the sum of the whole numbers. "actions fli-st, and to their sum add 
 
 220. 2^-K3|. 
 
 221. 3^4-2^. 
 
 222. 3^ + 5^. 
 
 223. 8J + 3J. 
 
 224. 4^ + 5|. 
 
 225. 5f + 3|. 
 
 226. 4| + 5^. 
 
 227. (ii + 2|. 
 
 228. 3^ + 4i. 
 
 229. 4i + 5i. 
 
 230. 2^+1. 
 
 231. 3J + 1. 
 
 232. 4^ Hj. 
 
 233. 31 +|. 
 
 234. 4i + |. 
 
 236. 101+3^. 
 
 236. lH+41 
 
 237. 12^ + 2 J. 
 
 238. 13f + l^j. 
 
 239. 18| + l|. 
 
 240 Add lOU, 30.51, 4021, 36H, and 222§. 
 
 241. Add 35J, 024f, 620i lOlSjl, and 1056i. 
 
 242. Add 65101, 2004i 6|, 3006^, and 113^. 
 
 243. Add 36^, 621^, 324f , 302f , 463^, and 2015J^. 
 
r - 
 
 48 
 
 SECOND 
 
 DEPARTMENT. 
 
 
 
 NoTB.— In order that fractions may 
 natoni and be partH of like nnitii. 
 
 be subtracted they 
 
 must have like denomi- 
 
 « 
 
 244. §-i 
 
 249. if-i 
 
 264. h - 1 
 
 269. A-i. ' 
 
 
 246. 1 - 1 
 
 260. i^-§. 
 
 266. J - 1 
 
 260. ^,-|. 
 
 
 246. ^-l 
 
 261. S-*. 
 
 266. R-f 
 
 261. ?-A. 
 
 
 247. i-l 
 
 262. §-i 
 
 267. l-f. 
 
 262. U-h 
 
 
 248. *-i 
 
 263. I-J. 
 
 268. ii-2. 
 
 263. A-^. 
 
 
 264. 2}i - 1 1. 267. H - 1 270. 2^ - ^. 273. m-H- 
 266. 3i-i. 268. 2|-ji. 271. 3i-l§. 274.10,^^-61. 
 266. «|-lii. 269. 3J-t. 272. 52-3j{. 276. 3^- if 
 
 276. 2051-67. 
 
 277. 324i{-48. 
 
 278. 673J-29. 
 
 286. 340§-42^. 
 
 286. 402^-13:i 
 
 287. 024f-G2|. 
 
 288. 225^-13J. 
 
 279. 222-35^. 
 
 280. 426 -37i. 
 
 281. 026-68^. 
 
 289. 2ni-ui 
 
 290. 303^ -m. 
 
 291. 424^-821. 
 
 292. 321J,-81|. 
 
 282. 364-lOOf. 
 
 283. 524-226^. 
 
 284. 312-196^. 
 
 293. 212|-112^. 
 
 294. 4031-314^. 
 296. 5G2|-421f. 
 296. «28f-210f. 
 
 -f 
 
 NoTB. — To multiply a fraction by a whole number, multiply the numerator or 
 di\-ide the denominator by that number. 
 
 297. |x8. 
 
 303. f X 16. 
 
 309. 
 
 ix22. 
 
 316. ^x4. 
 
 298. ^x7. 
 
 304. 1x18. 
 
 310. 
 
 ix24. 
 
 316. f\x2. 
 
 £99. ^x6. 
 
 306. fx20. 
 
 311. 
 
 ix36. 
 
 317. A X 7. 
 
 300. |xl2. 
 
 306. !x27. 
 
 312. 
 
 ix42. 
 
 318. H X 6. 
 
 301. fx21. 
 
 307. t X 15. 
 
 313. 
 
 ix64. 
 
 319. i?x8. 
 
 302. fx36. 
 
 308. fxl7. 
 
 314. 
 
 iV X 90. 
 
 320. Ux«. 
 
COMMON FRACTIONS. 
 
 49 
 
 ^ NOTB.— When the multiplioftnd la a mixed number multiply the fraction vtA 
 integ^er separately, and arid tho results. 
 
 321. 51x4. 
 
 322. 0gx5. 
 
 323. 8!J X 0. 
 
 324. 0^x8. 
 326. 4§ X 6. 
 
 326. 6| X 6. 
 
 327. nix 7. 
 
 328. tJifxS. 
 
 329. 7Jx9. 
 
 330. 8|x3. 
 
 331. 221^x4. 
 
 332. 3G2J X 3. 
 
 333. 655^x6. 
 
 334. 421Sx5. 
 836. 853^ X 8. 
 
 336. 321fx6. 
 
 337. 423Jx4. 
 
 338. C30Jx8. 
 
 339. 263|x5. 
 840. 100^x9. 
 
 341. 201| X 10. 
 
 342. 403| X 12. 
 
 343. 621^ X 18. 
 
 344. 369i X 25. 
 346. 624^x98. 
 
 346. 421^x47. 
 
 347. 328^x04. 
 
 348. 427§ X 86. 
 
 349. 025^x89. 
 360. 321Jx26. 
 
 Note.— Multiply by the numerator of the fraction, and divide the product by the 
 denominator. When the multiplier is a mixed number multiply by tho fraction 
 and integer separately, and add the results. 
 
 351. 103 x^. 
 
 362. 422 xi 
 
 363. 632 x|. 
 
 364. 321 x|. 
 366. 624 x|. 
 386. 683 xf. 
 
 367. 263 x2i. 
 388. 365 x3J. 
 369. 242 x4|. 
 
 360. 325 x5|. 
 
 361. 263 x3|. 
 
 362. 201 x5f. 
 
 363. 224x21f 
 
 364. 638x42f. 
 366. 219 X. 32.^. 
 
 366. 631xl9f 
 
 367. 298x32^. 
 
 368. 215 X laj. 
 
 NoTK.— Reduce mixed numbers to fractions ; cancel all factors common to the 
 numerators and denominators ; multiply the remaining: numerators for the numer- 
 ator, and the remaining denominators for the denominator. 
 
 369. ixfx|. 3'|3. §of 12x|of 16x|of 20. 
 
 376. f of 15 X I of 18 X ^ of 21. 
 
 370. f xfxf 
 
 371. - >|. 
 
 372. % ■^ 7 X ^. 
 
 373. ?x|x^3. 
 
 374. AxHxi 
 
 377. iof 18xf of 20xf of 27. 
 
 378. 2|x3ixifxfx4ixi. 
 
 379. 3ixT^x4|x/T><3§x22. 
 
 380. 8ixHx3|xi|x4ixi. 
 
f 
 
 50 
 
 SECOND DEPARTMENT. 
 
 Not*.- To divid* a fraetion by a whole number, divide the numerator or multiply 
 the denominator l)y that number. 
 
 381. 1^8. 384. K4. 387. H3. 390. !J^6. 
 
 382. i^2. 386. ^2. 388. K* 391. 8-^4. 
 
 383. K5. 386. K9. 389. A^9- 392. J-^2. 
 
 NOTK.— When the dividend is a mixed number divide the whole number and the 
 fraction separately, and odd the results. 
 
 393. 21,3i-r4. 
 
 403. 4210}- 
 
 -8. 
 
 413. 263^^12. 
 
 394. 321K3. 
 
 404;. 26325- 
 
 -2. 
 
 414. 32H-rl8 
 
 396. 6221^6. 
 
 406. 402ia- 
 
 -4. 
 
 416. 420f-16. 
 
 396. 220i-^(}. 
 
 406. 3032|- 
 
 -3. 
 
 416. 332|-h22. 
 
 397. 321 J -8. 
 
 407. <J200f- 
 
 -6. 
 
 417. 6011-25. 
 
 398. 101§4-9. 
 
 408. 2101A- 
 
 -3. 
 
 418. 423^-18. 
 
 399. 2161^7. 
 
 409. 1021^- 
 
 -5. 
 
 419. 6321-16. 
 
 400. 3211-8. 
 
 410. 6213^ 
 
 i-6. 
 
 420. 213f-19. 
 
 401. 0221^5. 
 
 411. 26311- 
 
 r9. 
 
 421. 212i-22. 
 
 402. 400^-8. 
 
 412. 2121}- 
 
 r2. 
 
 422. 1211-30. 
 
 Note.— To divide an integer, a fraction, or a mixe<l number by a fraction, invert 
 the terms of the divisor and proceed as in multiplication ; if by a mixetl number, 
 reduce the mixed number to a fraction before invertinf the terms. 
 
 423. K4- 
 
 424. Kl- 
 428. t^i 
 
 426. 5-^i 
 
 427. f-^i 
 
 428. i=V-i 
 
 431. 12^i 
 
 432. 18-f. 
 
 433. 16-|. 
 
 434. 29-f. 
 436. 18-f. 
 436. 26-f 
 
 429. A-^i 437. 29-f 
 
 430. A^f. 438. 18-i 
 
 439. 25 -2i. 
 
 440. 38-3i. 
 4U. 49-21. 
 
 442. 68-3|. 
 
 443. 99-2i|. 
 
 444. 87 ^3i 
 446. 46-li 
 
 447. 18^3^- 
 
 448. 22J-8I- 
 
 449. 331-3^. 
 
 450. l8*-2i. 
 
 451. 27i-3i. 
 
 462. 18f-3|. 
 
 463. 16^-li. 
 
 446. 28-3^. 454. 29^- U. 
 
COMMON FRACTIONS. 
 
 51 
 
 he 
 
 eit 
 er, 
 
 f 
 
 456. Change 32 to an equivalent fraction whose denominator 
 iB32. 
 
 466. How many poor families can be supplied with J of a ton 
 of coal each from 7f tons ? 
 
 467. The «um of three >j umbers is 84 ; the least is 4^, the 
 ^«<reate»t 47 J. What is the product of the three ? 
 
 468. What number diminished by | of itself leaves a remainder 
 of 240 ■{ 
 
 469. If § of a mill is worth $25^, what is | of the mill worth? 
 
 460. The sum of two fractions ij- ; one of them is J. What 
 is .'he other ? 
 
 461. What number diminished by | of f of itself leaves a re- 
 mainder of 580 ? 
 
 462. If f of a mill is worth $5225, what is J of the remainder 
 worth ? 
 
 463. Add ^ of a dozen to | of a hundred, and subtract the 
 sum from ^| of a thousand. 
 
 464. A lady bought 3 pieces of cloth ; the first contained 39| 
 yards, the second 28J yards, and the third 25^ yards. How 
 many yards in all ? 
 
 468. How many vests, each containing |,of a yard, can be 
 made out of 24 yards ? 
 
 466. If an acre of land is worth $28, what is | of an acre 
 worth ? 
 
 467. What fraction divided by § of 12 will give ^ for quotient? 
 
 468. A house and lot cost $2400 ; the lot cost } of what the 
 house cost. Find the cost of each. 
 
 469. Multiply 200002 by f and divide the product by |. 
 
 470. Divide 30103 by f and multiply the quotient by ^. 
 
 471. A man sold two houses for $1200 each ; on the one he 
 gained ^ of the cost price, and on the other he lost J of the cost 
 price. How much did he gain or lose on the two houses ? 
 
 tjrff^.V : 
 
52 
 
 SECOND DEPARTMENT. 
 
 III. DECIMALS. 
 
 HINTS AND DEFINITIONS. 
 A decimal fraction expresses one or more of the decimal divisions of a unit. 
 
 Decimal fractions, commonly called deeimaU, are usually expressed by writinjr 
 the numerator only. 
 
 The decimal 8lgn(.)or point detennines by its position the denominator oi 
 the fraction. 
 
 Annexinjf ciphers to a decimal does not alter its valud. 
 
 Each removal of the decimal point one place to the right multiplies the value of 
 the decimal by 10. 
 
 Each removal of the decimal point one place to the left divides the value of the 
 decinw' '•" 10. 
 
 A terminate decimal is one that either terminates, or can be made to termi- 
 nate, without a common fraction. 
 
 An Intermlnate decinial is one that cannot terminate without a common 
 fraction, expressed or understowl. ; 
 
 EXERCISES FOR MENTAL DRILL. 
 Note. — Do not use pen or pencil. 
 
 472. How many letters will it takt i write .008 in words ? 
 
 473. Find the sum of .08, .005, 2.3, 3.04, and .1, 
 
 474. Write the smallest decimal that can be expressed by the 
 figures 0, 5, 1, and 7. 
 
 475. Write the smallest decimal that can be expressed by the 
 figures 0, 0, 1, 2, 5, 3, and 0. 
 
 476. Find the difference between .05 and .025, 
 
 477. Ten times a certain decimal is .3. What is one tenth of 
 the decimal ? 
 
 478. Express ^ of one-hundredth as a decimal. 
 
 479. How many tenths in 50 hundredths ? 
 
 480. How many thousandths in 2 units ? 
 
 481. Find the difference between the two smallest decimals 
 ihat can be expressed by the figures 9, 8, and 2. 
 
 
DECIMALS. 
 
 53 
 
 482. f 
 
 483. |. 
 
 484. i 
 
 WRITTEN DRILL EXERCISES 
 DiRKCTioN.— Change to equivalent decimals. 
 
 485. I 488. ff. 491. I 
 
 486. /o 489. 2^\. 492. f 
 
 487. 
 
 1 
 
 490. 31. 
 
 493. i 
 
 494. H. 
 
 495. 6^V 
 
 496. T^ij,. 
 
 DiKKcTios.- Change to equivalent fractions. 
 
 497. .25. 500. .05. 503. .128. 506. .010. 609. .33^. 
 
 498. .75. 501. .375. 604. .875. 607. .025. 510. .16§. 
 
 499. .5. 502. .625. 606. .125. 508. .512. 511. .44*. 
 
 512. 
 513. 
 514. 
 515. 
 516. 
 517. 
 518. 
 519. 
 520. 
 521. 
 
 Direction. —Find the sum of the numbers in each exercise. 
 .321 ; 4.005 ; 32.062 ; 5.121 ; .005 ; .0006. 
 92 ; 2.05 : .025 ; 3.2 ; .001 ; .0051 ; 3.215. 
 3.6 ; 21.06 ; 191.04 ; 312.005 ; .05 ; .006 ; 9. 
 2| ; 2.5 ; 21.0^ ; 5.05 ; G.06 ; 3.05 ; 3J ; .9. 
 .005 ; 32.00005 ; 2,2 ; 30.03 ; 3000.1 ; .25 ; 8. 
 625 ; 300 ; .003 ; .025 ; 5.051 ; .5105 ; .256. 
 5.215 ; .00505 ; 3.3 ; 00.06 ; 311.01 ; 2^ ; 3| ; 25. 
 .251 ; .35^ ; .0^ ; .00.^ ; .00^ ; j ; .025 ; 100. 
 31.0005 ; 29800.0020 ; 31.012 ; 215.0152 ; 2.2. 
 3121.9 ; .99 ; .09 ; 99 ; 9.9 ; 200.009 ; .005 ; 21. 
 
 DiRBcrio.N.--Find the diflferenee between the numbers in each exercise. 
 
 522. 32.05; 9.005. 626. 1.1; .11. 
 
 823. 2.03J; 2.003i 527. 11 , .0011. 
 
 524. 9.25; .925. 628. 2| ; .05. 
 
 525. .003]; .30 0]. 529. 5| ; .05|. 
 
 530. 3.06^ ; 2.002. 
 
 531. 2.11^; 1.00|. 
 
 532. 42. Of ; 3.62f. 
 
 533. 3.01| ; .0014. 
 
54 
 
 SECOND DEPARTMENT. 
 
 I 
 
 DiRKxmoN.— Find the product of the numbers In each exercise. 
 
 634. 2.06 x^. 530. 3.21x2.31. 544. 21ix.21J 
 
 640. 9.99x90.9. 
 
 541. 2.06x.00i. 
 
 542. 4. 06 X. 03. 
 643. G.02x33J. 
 
 635. 3.004 X J. 
 
 636. 42.01 X .01. 
 
 537. 2. 6 X. 003. 
 
 538. 32.1 X. 06. 
 
 645. 9.021x100. 
 
 546. 21.39x1000. 
 
 547. .66§x.05. 
 648. 39.09x.06i. 
 
 NOTB. -Divide as in ordinary numbers, and point o«f from the right of the 
 quotient as many decimal places as the number in the dividend exceeds the number 
 in the divisor. 
 
 649. 2.06-2. 
 
 650. 30.5-^3. 
 
 651. 21.6^.3. 
 562. 3. 05 4-. 2. 
 553. 90.8-^.0l. 
 
 664. 36.9 -f- 9. 6. 
 666. 9.044-99.4. 
 656. 3(0. 12 -f 6. 21. 
 567. 4.21^5.12. 
 658. . 006 -f. 006. 
 
 559. .0062^.33^. 
 
 560. .0051-=-.16|. 
 
 661. .42-^2.12. 
 
 662. 9984.01 -r 2.1. 
 563. .1^.01. 
 
 564. From the sum of 22.62^ and 3.000^ take 10.059^. 
 
 665. To tlie difference between 5 and .6 add .06. 
 
 666. ^-.06 + i + . 6-. 025 + 1-^ + 2.03. 
 567. 12i- 2. 02 + 1-.001 + 2.1^.03 + 1 -.00*. 
 
 668. Multiply .006 by .06 and divide the product by 2. 
 
 569. How many letters will it take to write 2.005 in words ? 
 
 570. One hundred times a certain decimal is 2.003. What is 
 one-twentieth of the decimal ? 
 
 671. Find the product of the two smallest decimals that can 
 be expresst d by the figures 0, 0, 9, and 3. 
 
 872. The sum of two numbers is 20.02 ; one of them is 1000 
 times the other. What are the numbers ? 
 
 673. The product of two numbers multiplied by | is .0006 ; 
 one of the numbers is .05. What is the other ? 
 
 I 
 
 I ; 
 
 1 
 
 n 
 
i 
 
 BUSINESS EXERCISES. 
 
 55 
 
 
 IS 
 
 n 
 
 
 
 f/ 
 
 IV. BUSINESS EXERCISES. 
 
 MIXED NUMBERS. 
 Illustrative Exercise. 
 Find the cost of 234^ pounds of cheese at 9f cents. 
 234i 
 
 91 
 
 117i 
 
 2110i 
 
 $22. 57 A 
 
 Analysis.— t = J+i. Multiply 234J by i by dividing by 2. 
 Multiply 234i by J by dividing by 8. Multiply 234^ by 9 and add 
 the results. 
 
 NOTK.-In multiplying small numbers it will be found easier to reduce to frac- 
 tions and multiply in the ordinary way. The above method is well adapted to 
 commercial operations, in which the fractions are usually small. 
 
 574. 3| X 2i. 578. m X H- 582. 10^ x 2|. 586. 25J x 2|. 
 
 575. 4i X 31 579. 3| X 5^. 583. 18J x 3J. 587. 32| x 3J. 
 
 576. 2^ X 21 580. 12^ X 21 584. 15^ x 2J. 588. 45^ x H. 
 
 577. 3^x8i 581. ISixlOi 585. 23^x2^. 589. 32fx3i. 
 
 NoTE.-In the answers to the following business transactions the fraction, if 
 less than i, is omitted, and if J or more, J is added. 
 
 590. Find the cost of 203| pounds of tea at 37^ cents a pound. 
 
 691. What is the cost of 25| pounds of coffee at 18^ cents a 
 pound ' 
 
 592. Find the cost of 3021J pounds of ham at 12^ cents a 
 pound. 
 
 693. What is the cost of 2031^ bushels of wheat at $1.12i a 
 bushel ? 
 
 594. Find the cost of 1021 bushels of oats at 62J cents a 
 bushel, 
 
 595. Find the cost of 8312 yards of muslin at 37^ cents a yard. 
 
66 
 
 SECOND DEPARTMENT. 
 
 696. Find the cost of 32^ pounds of butter at m cants a 
 pound. 
 
 697. Find tlie value of 2993 pounds of sugar at 7S cents a 
 pound. " 
 
 699. Find the cost of 32| do.en eggs at 12^ cents a dozen. 
 
 600 Find the cost .,f 421^ bushels of oats at 27A cents a 
 bushel. 
 
 601. What is the value of (521 yards of sheeting at 8? cents a 
 y '.rd .' 
 
 DECIMALS. 
 
 Note. — To divide a deoimal bv 10 iim iiuwt ^f,. ^^ . . 
 
 . , , . "'=wii.«i uy lu, iw», iiKio, €tc rt'iiiovc the decimal noinf hm 
 
 602. Find the cost of 3235 pounds of coal at 16.25 a ton. 
 
 Nori..-If the third decimal figure in the product be less than 5, omit it and all 
 
 ollowm, .t ; ,f fi or more, add one to the second <K.ci„,al flKure and omit a^l olj 
 
 mfi:. A ton equals 20(K) pounds. • '""ow 
 
 603. Find th.3 cost of 4325 pounds of coal at $5.75 a ton. 
 
 604. Find the cost of G984 pounds .)f coal at |4.85 a ton. 
 606. Find the cost of 21,535 pounds t)f coal at $5.25 a ton. 
 
 606. Find the cost of 6284 feet of lumber at 112.35 a M. 
 
 607. Find the cost of 930 feet of lumber at #2.37i a hundred. 
 
 608. Fi ad the cost of 936 feet of lumber at $24.25 a M. 
 
 609. Find the cost of 8463 feet of lumber at $27.36 per M. 
 810 Find the cost of 3684 pounds of pork at $9.24 a hundred. 
 
 611. Find the cost of 945 pounds of pork at $8..32 a hundred. 
 
 612. Find the cost of 837^ pounds of beef at $6.48 a hundred. 
 
 613. Find the cost of 428 pounds of bran at 75c. a hundred. 
 
 (i 
 
BUSINESS EXEKCISES. 
 
 67 
 
 614. Find the cost of 8462 pounds of hay at «>22.50 a ton. 
 
 615. Find the cost of 6521 pounds of hay at $43.25 a ton. 
 
 616. Find the cost of 2198 pounds ..f straw at $9.55 a ton. 
 
 617. rmd tlie cost of 6225 bricks at $8.25 a thousand. 
 
 618. Find the cost of 4760 envelopes at $1.37 per thousand. 
 
 619. Find the cost of 3260 latli at 18|c. a hundred. 
 
 «i??^Kn^"''^.u""' '"'* ''^ «*>"«tructing 5984 feet of sidewalk at 
 $ld7.50 per thousand feet. 
 
 SHORT METHODS. 
 Illustrative Exercises. 
 
 1. Find the sum of ^ and |. 
 
 3 + 4 = 7 ) ^ , Here there are two fractions, and the numerator is 1 in 
 
 3x4= 12 J ^^ each case. To find their sum, aid 3 and 4 (or the numer- 
 
 ator and multiply them for the denominator. 
 
 2. Find the difference between J and {. 
 
 3x4=12/ ~" 
 
 3. Find the sum of 3 and ». 
 
 2x0 = 10 I ,„ 
 
 3x3= 9 / "" numerator. 
 
 3x5 = 15 = denominator. 
 
 Here there are two fractions, and the numerator is 1 in 
 each case. To find the- difference, subtract 3 from 4 for 
 the numerator and multiply them for the denominator 
 
 U=IA. 
 
 Here the numerators are Rreater than 1. 
 To find the sum of tlie fractions, multiply 
 the numerator of the first by the denomi- 
 nator of the second, and the denominator of 
 the first by the numerator of the second, and 
 add the products for the numerator of the 
 answer. Multiply the denominators for the 
 denominator of the answer. 
 
 4. Find the difference between * and ^ 
 
 2x6=101 , 
 
 3x3= 9| = '=n"merator. 
 
 3x5= 15 = denominator. 
 iV = difference. 
 
 To find the difference between the frac- 
 tions, subtract after multiplying, instead 
 of adding. 
 
 I 
 
58 
 
 SECOND DEPARTMENT. 
 
 621. ^ + J. 
 
 622. h + l 
 
 623. i + i- 
 
 624. Hi 
 626. i + i. 
 
 626. i + f 
 
 627. i + i 
 
 628. li+f. 
 
 629. i + J. 
 
 630. HI. 
 
 631. i + f 
 
 632. Hi 
 
 NoTB.- -Do not 
 
 633. Hi^ 
 
 634. HI. 
 636. H^^ 
 
 636. Hi 
 
 637. Hi 
 
 638. i-i 
 
 639. i - i 
 
 640. Hi 
 
 641. h - i 
 
 642. js-i. 
 
 643. i^-^i 
 
 644. Hi. 
 
 u«ie pen or pencil. 
 
 646. Hi 
 
 646. Hi 
 
 647. Hi 
 
 648. ii + l 
 
 649. Hi 
 
 660. Hi 
 
 661. Hi 
 
 662. i + 1 
 
 663. Hi 
 
 664. Hi 
 666. Hi 
 666. Hi 
 
 667. Hi 
 
 668. Hi 
 
 669. I - i 
 
 660. Hi 
 
 661. I - i 
 
 662. f-i 
 
 663. I - i 
 
 664. Hi 
 666. Hi 
 
 666. fi 
 
 667. Hi 
 
 668. I - i 
 
 V. REVIEW. 
 
 EXERCISES IN ANALYSIS. 
 669. If 5 poiuuls of tea cost |3.25, wliat will 9 pounds cost ? 
 .") pounds cost $.3.2'), 
 1 pound C0S1 . .-3.2o-r5 = 65 cents, 
 9 pounds cost 65 cents x 9 = $5. 8."), 
 
 cos?f ' " ^ ^''""''' '*^ *'"**'''' '°'* ^^•^^' "^^"^^ ^'^^^ -^ P«»«'^« 
 
 671. If 27 yards of cloth cost $12.42, what will 113 yards cost? 
 
 672. If 12 men can do a piece of work in 42 days, in how 
 many days can 28 men do it ? 
 
 12 men can do the work in 42 days, 
 
 1 man can do the work in 42 x 12 = 504 days, 
 
 28 men can do the work in 504 elays^ 28-= 18 days. 
 
REVIEW. 
 
 59 
 
 tak?40 le^roTJuiu"' ' '""^^ ^^^^^^^^i^l^n, will it 
 
 676 If it reciuire 260 busJiels of wheat to make 50 barrel* of 
 flour, how many bushels will be required to make 19 ba"!? 
 
 JltlT::? ^' ^^"' ^^^^ '"'''^ -'^' -"^ ^^^ -- cost 
 
 677. In what time will a boy, at 37A cents a day, earn as much 
 H8 a man earns in 75 days, at $2. 27 a day ? ^ 
 
 the Ia;m" ^ "' ' ''^"^ '^ ""^^' ^'''' ^^^* ^« *^- value of § of 
 
 679. If A of a bin of coal be worth 863, what is ^ of it worth ? 
 
 680. If f of a pound of tea cost 50c. , what will 1G| pounds cost ? 
 
 681. A dram is dug by 45 men in Ofi rln,r« . r, 
 
 would have been roqulred to dig itTn 25 dt^s ^ '^" ""'^^ "^^" 
 
 of rwLLt:^;'f ^ '^ ^^"'^ ^^^^' -^-^ ^« ^^^ -^- 
 
 683. A firm had i of its capital invested in goods i of ih. 
 remainder m land, and the remainder, $1224, in ca 'h m J 
 was the capital of the firm ? ^^* 
 
 684. If the 4-pound loaf cost 9 cents when flour is 85 50 a 
 barrel, find its cost when flour is $7 a barrel. 
 
 685 If 24 pounds of rice are worth as much as 18 pounds of 
 
 ZgarT ''""''' '^""'^ '' ''-' '-' --'^ - --h - ^iTpouLs 
 
 686. If 12 men earn 872 in one week, how much will 18 m«n 
 earn, at the same rate, in the same time ? '" 
 
 687. If 2| yards of broadcloth be worth «9^ in i ^ • .^ 
 value of 16J yards at the same rate ? ^ ''' "^^'' " '^' 
 
 688. If I of an acre of land cost 860, what will ) 
 at the same late ? 
 
 acres cost 
 
 : 
 
\ 
 
 60 
 
 SECOND DEPARTMENT. 
 
 MISCELLANEOUS EXERCISES. 
 
 689. What are the prime factors of 25920 ? 
 
 690. Find tlie H. C. F. of 235 and 686. 
 
 691. Find the L. C. M. of 3, 25, 60, and 100. 
 
 692. Find the greatest number that will divide 392 and 257, 
 leaving as remainders 7 and 12. 
 
 693. What is the H. C. F. of 182, 364, and 455 ? 
 
 694. Four cheeses, weighing respectively 32| pounds, 41^ 
 pounds, 37 1 pounds, and 51 pounds, were sold at 22 cents a 
 pound. How much was received for them ? 
 
 / 695. Five-sevenths of i of a number is 75. What is the 
 
 ^ number ? 
 
 > 
 
 696. Write down all the common multiples of 720 and 1008 
 that are less than 30000. 
 
 697. Divide .012261 by 2.01. 
 
 698. A can cut 1| cords of wood in ^ of a day ; B can cut as 
 much in ^ of a day as A can cut in | of a day. How long will it 
 take them to cut 30 cords working together ? 
 
 699. The H. C. F. of two numbers is 17, and their L. C. M. 
 is 3876. One number is ^04. Find the other. 
 
 ^ 700. I spent ^ of my money and ^ more, then ^ of the 
 remainder and $6 more, then | of what was left and $16 more. 
 I then had $18. How much had I at first ? 
 
 701. A farmer sold 24 dozen eggs .it 22^ cents a dozen, and 12 
 ^ pounds of butter at 27^ cents a pound. He was paid in tea at 
 
 87 cents a pound. How many pounds of tea should he receive ? 
 
 702. Find three numbers less than 125 which are multiples of 
 both 12 and 18. 
 
 703. A gentleman gave away | of the books in his library, 
 lent i of the remainder, and sold ^ of what was left. He found 
 that he had 400 books remaining. How many had he at first ? 
 
REVIEW. 
 
 61 
 
 the clotlies / ciotiies. What was the value of 
 
 JT.-J!:r^z:zz "for:: rr^ -^-f ""^ "«■■"■ °- 
 
 «;. « „„e, an W. WHe., „„, tI;Mri:il t 
 
 oanTi-o'50"LXu1/: r-'-Hf "T '" " '"'^■' ""O »« 
 and piok in 6 days ? ^' "^^ *""'"='» '^'"' h" dig 
 
 eair JdT "r^u' ;; rr :r "^r r '•'" " -»'" 
 
 How many persons were therl ? ^'^ "" '<""'»'^>* «-6«. 
 
 709. A man and his wife use a hno- r.f « • ^. , 
 
 the jnan is away a ^ of Ho: UstsI 'w f^^^^^^^ ?'" 
 would -t last the man if alone ? '^ """ '™8 
 
 710. Divide J26J acres of land among A B and P ' • ^ 
 7J acres more than B, and B I2i acres ,Lt ,tn A *'"* 
 
 in "ilyt "Sot L7:i,nrrt '■;/ ■'''^» ^ ^ - d» '^e sa„.e 
 long wdl ,t take them to do the work jointly » 
 
 712. A sold to B a watch fnv i ^ xi. 
 it to for *36, which was 1 Ku "" " •»'* ''™- » sold 
 
 pay for it ? ' ^ '"'' *"" " •="" W"'- What did A 
 
 and quotient ? ' « • '» me ±i. t,. J^ . of the divisor 
 
62 
 
 SECOND DEPARTMENT. 
 
 f 
 
 -P 
 
 715. Find the least number of aoldiera that can be divided 
 into CO- ranies of IG, 30. 48, 56, or 72 ? 
 
 716. A fine of ^7 had to be raised among a number of boys. 
 One-fourth of them paid 5 cents each ; one- fourth paid 9 cents 
 each ; one-fourth paid 10 cents each ; and the others 11 cents 
 each. How many boys were there ? 
 
 717. Find the least number which, when divided by 3, 4, 6, 
 or 9, gives 2 as a remainder in each case. 
 
 718. Find the greatest number that will divide 2293, 4246, 
 and 6348, leaving 18, 20, and 23 respectively as remainders. 
 
 y 719. If a turkey weighing 9| pounds costs $1.33, what should 
 '^one cost that weighs 14| pounds ? 
 
 720. There is a number that will divide every one of the 
 numbers 637, 504, 766, ahd 1001. What is it ? 
 
 721. If \ of the time since midnight is equal to \ of the time 
 since noon, what time is it ? 
 
 722. What number is that to which if f of itself plus 42 be 
 ^^^dded, the result will be three times the number ? 
 
 723. The marbles in a box can be made into groups of 17 and 
 none remain, but when made into groups of 16, 18, or 24, 9 re- 
 main in each case. How many marbles are there ? 
 
 724. What number taken from the sum of 10| and 12^ will 
 leave 5| ? 
 
 725. A piece of cloth when measured by a yard measure which 
 is .6 of an inch too short appears to be 88| yards long. What is 
 its true length ? 
 
 726. Find the smallest number which, when divided by any 
 number between 10 and 20, will leave a remainder. 
 
 727. Three persons, B, C, and D, bought a city lot for $10,400, 
 of which B paid $3200, C $2400, and D $4800. What part of 
 the lot belongs to each ? 
 
 728. By what number must .001 be multiplied to produce 22| ? 
 
■_ REVIEW. Q^ 
 
 to H ti.e. the „H«.„a. a...,.,. VLT^:^„.,Z'z::r' 
 
 780. i-05 + i + . 5-. 025 + 1-^ + 2.03-. 01. 
 731. The sum of two numbers is l.^ii'7 tk : i-a- 
 of the smaller nu.nber. VVhatrrnuJer/'^^""^ '' ^ 
 
 of !?^'i '^^^ '"'" f ^''^ ''""^"^•^ ^« ^«^«- Their difference is « 
 of the larger number. What are tlie numbers ? ^ 
 
 733. ^inJ the sum of all the^o/^er fractions that can be formed 
 hav.ng onl, one figure in the numerator and one in the d^^t 
 
 N0TK.-The denon.i„ator of a proper fraction is greater than the nun,erator. 
 
 734. Divide f 28, 217 betwp«n tur« «,« • • 
 
 the other receives. ™'"' ^'"^"^ ""« ^ «^ ^h«* 
 
 ,736. A, B and C have 640 acres of land. One-third of A's 
 V «hare is equal to i of B's and 3 nf R'u d • , oi a s 
 
 1 y ui jD 8, ana | ot J3 s share is equal to S- of f!'« 
 
 How many acres has each ? to f oi u s. 
 
 736. If 1 of the time past midnight is equal to \ of the time 
 until noon, what time is it ? ^ "® 
 
 737. Divide $490 between two men, giving one «.S .« ff 
 
 the other gets U. ^ ^ ^ ^^ ''^**'" ^ 
 
 738. The sum of two numbers is 3150, and one bears the same 
 relation to A as the other does to |. Find the numbers. 
 
 739. Divide 279 acres among A, B, and C, so that B may get 
 -■ twice as much as A, and C three times as much as B. ^ ^ . 
 
 740. Three men hired a pasture for $42. The first nnt ,•» ^ 
 
 boat valued at $5900 The br,a+ ^o k i , , ' 
 
 w^uv. ine boat was burned shortly aftpr ih^ 
 sale. How much did he lose ? ^ 
 
64 
 
 SECOND DEPARTMENT. 
 
 ii 
 
 742. Two persoriB join in purchasing some property, one pay- 
 ing $1250 and the other moOO. If the property rise in value to 
 IKJTSO, what will be the value of each one'« share . 
 
 743. Bell metal contains 78 parts copper unci 22 parts tin. 
 What weight of each of these metals will there be in a bell 
 weighing 490 pounds ? 
 
 744. An army of 12,000 men has provisions for 24 days. How 
 long will these provisions last if the army is reinforced by *M)00 
 men ? 
 
 746. A, B, and C together have $<}45. C has twice as njuch 
 money as B, and if $12 be deducted from A's money it will be 
 }f of B's. How much has each ? 
 
 746. Divide $375 among 2 men, 3 women, j.nd 4 boys, so that 
 as often as each boy getSj$2, each woman may get $3, and each 
 
 man $4. 
 
 747. A farmer bought three farms of 200 acres each at $5.26 
 an acre. He built three barns, one on each, at a cost of $736 a 
 farm, and 920 rods of fence at $2.50 a rod. He spent $125 in 
 improving the houses. He then sold the farms at $11.26 an 
 acre. Did he gain or lose, and how much ? 
 
 V48. A man walked from A to B at the rate of 3^ miles an 
 hour, remained there an hour and a half, rode back at the rate 
 of 8 miles an hour, reaching A 14 hours after Iv started. How 
 far is it from. A to B ? 
 
 749. Bought 60 geese and turkeys for $53, paying 75 cents 
 each fr the geese. How many turkeys did I buy, and at what 
 price ? 
 
 760. A drover bought 100 sheep and calves for $387, paying 
 $4.50 each for the sheep. Had the number of sheep and calves 
 been interchanged they would have cost $413. How many wer*' 
 there of each ? 
 
 > 
 
THIBD DEPAKTMENT. 
 
 I. MEASURES. 
 
 HINTS AND DEFINITIONS. 
 
 ancfl^'^Str''^' " ""''" "•"'^'^'"'^-" ""^'- --P* P-'0« -UU 
 
 One ton cqu»lg twenty hundredweight, or 2000 pounds 
 yJ::ZlT2Z:^::!r'''- «'-»--''-•«" pound. Aharre.o,h«eror 
 
 dis^c"" """"'^' '" """* '" "^""'•'"'^ '«"**'•«• *'-*d*»',. depth,, height., or 
 One mile U equal to 320 rods, or 1760 yards, or 6280 feet. 
 One rod is equal to 5i yards, or IflJ feet. 
 There are 12 inches in a foot, and 3 feet in a yard 
 AshoemaJcer-ssl^aisone-thirdof an inch. A hand is 4 inches. A fathom Is 6 feet 
 
 The unit of measurement is the chain, which is 4 rods or 66 feet long 
 There are 100 links in a chain, and a mile is equal to 80 chains 
 _Bq^^Te measure is used m measuring surfaces, such as land, boards, plaster- 
 
 There are 144 square inches .n a square fo3t. and 9 .quare feet i , a square yard. 
 
 There are 30i square y.rds in a square rod, and 160 square rod. in an acre 
 
 Surveyors' square measure is used in measuring land. 
 
 There are 10 square chains in an acre, and 640 acres in a sqJare mile. 
 
 Liquid measure is used in measuring liquids 
 
 There are 4 gills in a pint, 2 pints in a quart, and 4 quarts in a gallon. 
 
 There are 31J gallons in a barrel. 
 
 Dry measure is used in measuring dry articles. 
 
 There are 8 quarts in a peck, and 4 pecks in a bushel 
 
 an Jtronr;uid'l\;::7 ™"^"" ^^^^ ^'""^ * «^-^-'" -^-^^^ '»>- t^e quart 
 
 .e:^sSrj:r^:;::^rr^"""^^^"'"«'^^''--^"-*«-^^^ 
 
 There are 12 units in a dozen, and 12 dozen In a gross. 
 
 There are 24 sheets of paper in a quire, and 20 -luirea in a ream. 
 
 I 
 
 'I 
 
66 
 
 THIRD DEPARTMENT. 
 
 PRACTICAL EXERCISES. 
 
 1. Find the value of 280 pounds of oat meal at 45 cents a 
 stone. 
 
 What will a hundredweight of beef cost at 18J cents a 
 pound ? 
 
 3. How much should a farmer receive for 3 tubs of butter, 
 each containing 63 pounds, at 22 cents a pound 1 
 
 4. Find the cost of 427 pounds of rice at 64 cents a stone. 
 
 5. What will 18 pounds of baking powder cost at 2^ cents an 
 ounce. 
 
 6. If 25 pounds of coal cost 15 cents, what will 2 tons of 
 coal cost ? ' 
 
 7. A grocer buys 3 tubs of butter, containing 84 pounds each, 
 for $37.50, and sells the whole at 18 cents a pound. How much 
 does he gain or lose ? 
 
 8. A butcher buys a barrel of pork for $24, and sells the whole 
 at 19 cents a pound. Find his profit. 
 
 9. Find the cost of 18 tons of hay at 75 cents a hundicd- 
 weight. 
 
 10. Find the cost of 56 ounces of candy at 18 cents a pound. 
 
 11. How much will 924 pounds of feed cost at $1.50 a hun- 
 dredweight 1 
 
 12. A li'.id of hay with the wagon weighs 2348 pounds. The 
 wugoii weighs 829 pounds. Find the value of the hay at $24.50 
 a ton. 
 
 13. A barrel of beef which cost $18.75 is retailed at 12| cenls 
 a pound. How much is gained ? 
 
 14. Find the cost of 375 pounds of straw at 25 c-nts a hun- 
 dredweight. 
 
 15. What will 5680 pounds of bran cost at $27.50 a ton ? 
 
 
i 
 
 MEASURES. g7 
 
 16. Find the cost of 2985 pounds of bran at 54 cents a hun- 
 dredweight. 
 
 - T. .-Grain, geeds, and similar produce, are usually sold by the bushel Th« 
 numuer Of pounds in a bUshel differs in different States and ProSces The 
 exercises given in this book are based upon the following table :- 
 
 ^"■'^^ "^ '*'«• •" California, 50 ; Louisiana, 32 ; Mas^^aohusetts, Ver- 
 
 «,. . '"«"* and Oregon, 46 ; Pennsylvania, 47. 
 
 *^''<»* 60 lbs. In Connecticut, 56. 
 
 ®**' 32 lbs. In Canada, 34 ; ( ccticut. 28 ; Iowa, 35 ; Maine 
 
 Massachuse^s, Aorth Carolina and New Jersey' 
 
 30 ; Kentucky, 33^. 
 
 ^ '^'- ^" ""nois and California, 52 ; New Hampshire, 54 • 
 
 New York, 58. 
 
 "^^'^ -56 lbs. I,. !alifornia and Illinois, 54. 
 
 Pfeas 60 lbs. 
 
 Clover Seed 60 lbs. In New Jersey, 04. 
 
 Tin.otny Soed. . . .45 lbs. In Canada, 48 ; New York, 44 ; Wisconsin, 40. 
 
 DiRECTioN.-In the exercises which follow, the cost or selling price of the ^rain 
 
 17. Wlieat— 1240 pounds at 90 cents a busliel. 
 
 18. Wheat— 2150 pounds at 85 cents a bushel. 
 
 19. Wheat— 3265 pounds at |1.20 a bushel. 
 
 20. Wheat— 6428 pounds at $1.12 a bushel. 
 
 21. Wheat— 3529 pounds at $1.15i a bushel. 
 
 22. Wheat— 5965 pounds at $1.02 a bushel. 
 
 23. Bailey— 3246 pounds at 88 cents a bushel. 
 
 24. Barley— 6487 pounds at 9^ cents a bushel. 
 26. Barley— 4005 pounds at 39 cents a bushel. 
 
 26. Com— 5684 pounds at 58 cents a bushel. 
 
 27. Corn— 2469 pounds at 88 cents a bushel. 
 
 28. Corn— 3425 pounds at 72 cents a bushel. 
 
 29. Corn— 5680 pounds at 99 cents a bushel. 
 
 30. Oata — IrtOn nonnri'- af ^^^ f ' u i 
 
 -- ["u»!!u,T til- rjij xsciita a uushel. 
 
68 
 
 THIRD DEPARTMENT. 
 
 31. Oats — 2669 pounds at 66 cents a bushel. 
 
 32. Peas — 9840 pounds at ()4 cents a bushel. 
 
 33. Rye — 2486 pounds at 98 cents a bushel. 
 
 34. Rye — 3215 pounds at 92 cents a bushel. 
 36. Rye — 4621 pounds at 75 cents a bushel. 
 
 36. Clover Seed— 1984 pounds at $2.90 a bushel. 
 
 Note. — In a few cities produce is bought and sold by the cental of 100 pounds. 
 
 37. When wheat is quoted at $1.20 a bushel, how much is it 
 worth per cental ? 
 
 38. When corn is quoted at 90 cents a bushel, how much is it 
 worth per cental ? 
 
 S9. V/hon barley is quoted at 96 cents a bushel, how much is 
 it worth per cental ? 
 
 40. When wheat is quoted at $1.37^ per cental, what is it 
 worth per bushel ? 
 
 41. When corn is quoted at $1.10 per cental, what is it worth 
 per bushel 'I 
 
 42. A produce dealer buys 3360 pounds of wheat in Mm' sa- 
 chusetts at $1.16 per bushel, and sells it in Connecticut at cie 
 same price. How much does he gain ? 
 
 43. A produce dealer buys 4480 pounds of oats in Iowa at 
 63 cents per bus'iel, aud sells the same in Illinois at 00 cents. 
 Does he gain or lose, and Iiow much ? 
 
 44. A produce dealer buys 6600 pounds of oats in Kentucky 
 at 54 cents, and sells the same in North Carolina at 65 cents. 
 How much d- 3 he gain ? 
 
 46. A dealer in corn buys 22,736 pounds in New York State 
 at 72 cents, and sells the same in Ohio at 75 cents. How much 
 does he gain ? 
 
 46. A dealer in barley buys 27,830 pounds in California at 
 93 cents, and sells the same in Oregon at ^1. How much does 
 he gain ? 
 
MEASURES. 
 
 69 
 
 47. Find the total weight, in pounds, of 
 
 Three tons of hay and two tons of straw. 
 
 Twenty-four ounces of iron and 32 ounces of lead. 
 
 Four stone of oat meal and 3 stone of rice. 
 
 A barrel of beef and a barrel of flour. 
 
 Three bushels of wheat and 4 bushels of barley. 
 
 A cental of oats and a bushel of corn. 
 
 48. How many inches are there in 3^ rods ? 
 
 49. How many inches are there in a chain ? 
 
 50. A horse is 15^ hands high ; how many inches high is he ? 
 61. A lake is 112^ fathoms deep ; how many feet deep is it ? 
 
 52. How many yards in 24 chains ? 
 
 53. How many links are there in 110 yards ? 
 
 64. How many inches are there in three miles ? 
 
 56. Find the cost of 20 miles of telephone wire at 35 cents a 
 pound, supposuig one pound stretches 80 feet. 
 
 56. Find the cost of 4 miles of barbed wire at | cents per 
 
 foot. '■ 
 
 57. Wliat will it cost to survey 25 miles of road at 25 cents a 
 cham ? 
 
 58. What is the cost of a cable 921 feet long at 95 cents a yard ? 
 69. Find the total length, in feet, of 
 
 180 rods, 22 yards, 3 miles. 
 
 55 inches, 10 hands, 8^ fathoms. 
 
 12 chains, 3 sizes, 160 links. 
 
 60. How many st^uare inches are there in a square yard ? 
 
 61. How many square feet are there in a square chain ? 
 
 62. How many square rods are there in 250 square chains ? 
 
 63. Find the cost of 15 square yards of canvas at 12 cents a 
 square foot. 
 
 N 
 
70 
 
 THIRD DEPARTMENT. 
 
 64. Find the cost of 221^ yards of cloth at $1.32 a yard. 
 
 65. Find the cost of 18 square feet of gold leaf at 2A cents a 
 square inch, 
 
 66. Find tlie cost of a square mile of farm land at «4 25 an 
 acre. 
 
 67. What will 3200 8(iuare rods of land cost at $1.26 per 
 square chain ? 
 
 68. How many pints of oil in a vessel containing 15 gallons ? 
 . 69. A fruit dealer bought 5 bushels of cherries at $2.50 a 
 
 ^\ bushel, and sold them at 15 cents a quart. Did he gain or lose 
 and how umch ? ' 
 
 70. How many quarts of ben =os are tliere in 12 pails, if each 
 contain | of a peck ? 
 
 71. What is the v^lue of 3426 bushels of potatoes at 42 cents 
 a peck ? 
 
 72. A grocer bought a b«,rrel (31| gallons) of syrup for $7.50. 
 He sold half of it at 18 cents a quart, and the remainder at 22 
 cents a quart. How much did he gain ? 
 
 73. How many weeks are tliere in the years 1884, 1885, 1886, 
 
 74. How many hours are there in 3 weeks ? 
 
 \ 76. How many minutes from 7.30 p.m., Monday, until 3 15 
 n a.m., Tuesday. 
 
 76. How many minutes from 2.35 p.m., Saturday, until 8 43 
 a.m., Monday ? 
 
 . . 77. How many hours from 1. 22 a. m. , February 24, 1885, until 
 I 0.22 p.m., March 3, 1886? 
 
 78. How many leap years between 1775 and 1905 ? 
 
 79. A boy bought a gross of penholders for 80 cents, and sold 
 them at 3 cents each. How much did he make ? 
 
 80. How many sheets of paper in 3 reams ? 
 
 ! 11 ! 
 
 ii 
 
CURRENCY. 
 
 71 
 
 81. A stationer bought 4 roams of foolscaj) at $2.75 a ream 
 and sold half of it at 25 cents a quire and the remainder at the 
 rate of 4 sheets for 5 cents. Find his entire profit. 
 
 82. Find the coat of 25 gross of writing-pads at 75 cents a 
 dozen. 
 
 II. CURRENCY. 
 
 HINTS AND DEFINITIONS. 
 
 pa^entT/de?tf ^^''**" '' ^^""^'"^ '"^ "'""''' '"'''"^ "*^ **" ^^^'^ ""^''^ '" *»"■' 
 Sterling money is the name applied to the legal currency of Great Britain 
 The unit of this currency is the pound (£) or aovereiffn, the vaiue of which in 
 
 dollars and cents is $4.86g. "-'"on in 
 
 There are 12 pence (d.) in a shilling («.) and 20 shillings in a pound. 
 
 t.^ n TT^ '' ''"'•*'"*••*"'■ *" * P«""d- "^"^ -^ guinea is equal to 21 shillings, or 
 ♦n.ll in American currency. 
 
 The franc of France, Belgium, and Switzerland is equal to about 19i cents. 
 The crown of Norway, Sweden, and Denmark is equal to about 26} cents. 
 The mark of Germany is equal to about 23J cents. 
 
 EXERCISES FOR MENTAL DRILL. 
 Note.— Do not use pen or pencil. 
 
 83. How many five-cent pieces in $12 ? 
 
 84. How many pence are there in £3 ? 
 
 85. Write the value of an English crown in cents. 
 
 86. Write the value of two guineas in dollars and cents. 
 
 87. What is the difference in value between two guineas and 
 one eagle ? 
 
 88. What is the difference in value between a pound sterlinir 
 and five dollars ? *^ 
 
 89. What is the difference in value between four marks and 
 one dollar ? 
 
11 
 
 ! 
 
 lli M 
 
 :*ii 
 
 
 72 
 
 THIRD DEPARTMENT. 
 
 90. What is the difference in value between a franc and n 
 quarter of a dollar ? 
 
 91. What is the difference in value between an English and a 
 Danish crown ? 
 
 92. A boy has three sovereigns, four half-dollars, and five 
 murks. His money is equal to how many cents ? 
 
 BUSINESS EXERCISES. 
 
 NoTB.-The following: method of reducing shillings and pence to the decimal of 
 a pound is suffloiently accurate for most business purposes :— 
 
 Write onthalf qf the !,reate»t even number of shillings as tenths, and if there be 
 an odd shilling write five hundredths; reduce the pence to farthings, and write 
 their number as thou8a7idths. If the number of farthings is between IS and S6 
 add 1 to the thousandths ; i/ between 36 and IS, add S to the thousandths. 
 
 Illustrative Exercises. 
 
 1. Re<luce £3 148. 6d. to the dec-aial of a pound. 
 
 Put down the f 3 ; then divide the 14 by 2, and put down 7 ; then multiply 6 by 
 4 and add 1. The result will stand thus : £3.726. 
 
 2. Reduce £4 ISs. lOd. to the decimal of a pound. 
 
 In this exercise one-half of 15 is 7J, an uneven number. We put it down In the 
 decimal form : .75. Four times 10 are 40 ; add 2 and we have 42, or .042, which, 
 added to .76, gives .792. Th^ work will stand thus : 
 
 £4 158. 10d.= £4.752 = £4.792. 
 
 DiRRCTioN.-The shillings and pence in the following exercises are to be reduced 
 to the decimal of a pound by the method explained above. 
 
 93. £2 38. Gd. 
 
 94. £4 6s. 5d. 
 96. £8 78. 4d. 
 
 96. £9 3s. 5d. 
 
 97. £4 78. 8d. 
 
 98. £2 Ss. 7d. 
 
 99. £3 3s. 9d. 
 
 100. £2 Is. lid. 
 
 101. £3 28. lOd. 
 
 102. £4 38. 9d. 
 
 103. £6 48. 8d. 
 
 104. £C 5s. 7d. 
 106. £7 68. lOd. 
 106. £8 78. lid. 
 
 107. £12 lis. 9d. 
 
 108. £22 12s. 8d. 
 
 109. £25 13s. 7d. 
 
 110. £24 14s. 6d. 
 
 111. £23 15s. 7d. 
 
 112. £22 168. 5d. 
 
 113. £31 17«. 8d. 
 
 ! |M' 
 
CURRENCY. 
 
 73 
 
 NoTK.— When money u at par value, and f( nearly all practical purposes, the 
 followlnsr i» the best o<-i shortest method of re<lucing Entrlish money to dollars 4nd 
 cents :— 
 
 The pound sterlinK is «|ual to IJ4.868. .Now, 80 Is J of 
 400, and (iff is ,\, of 80. Then, to multiply by 4861, mul- 
 tiply by 400, divide the product by 5 and place the quo- 
 tient under ; then divide this quotient by 12, and place 
 the second (juotient under the first. Add, and the sum 
 will be the same as though the number were multiplied 
 by 486i| in the ordinary way. 
 
 $4.00 
 
 .80 = i of 400. 
 
 Illustrative Exercise. 
 Find the value of £3.725 in dollars and cents, 
 £3.72ox4.8(jg 
 £3.725 
 
 5 
 12 
 
 14.900 
 
 2.980 
 
 .248 
 
 Multiply by 4 for the dollars. Then divide this product 
 by 5, which is equivalent to multiplying £3.725 by .80 ; 
 and dividing 2.98 by 12 is equivalent to multiplying £3.725 
 by .Oflji, for j'j of J of 400 is Og. 
 
 118.128 
 DiREOTio.v.— Find the value of the following sums in dollars and cents :— 
 
 114. £2.643. 119. £2.213, 
 
 115. €3.425. 120. £4.421. 
 
 116. £4.216. 121. £5.563. 
 
 117. £5.310. 122. £6.428. 
 
 118. £8.214. 123. £9.365. 
 
 124. £0.432. 129. £12.219. 
 
 125. £0.569. 130. £16.190. 
 
 126. £0.982. 131. £18.263. 
 
 127. £0.846. 132. £21.508. 
 
 128. £0.912. 133. £13.009. 
 
 134. Find the value in dollars and cents of a P. O. money 
 order for £2 6s. lOd. 
 
 136. Find the value in dollars and cents of a P. O. money 
 order for £12 138. 4d. 
 
 136. What is the value in American currency of 800 crowns of 
 Denmark ? 
 
 137. If 5 shillings be worth ^1.22, how much should one re- 
 ceive for an TCnorlisli P O mfino-i^ .^f/l^^o f^^ i>oa ii- cj o 
 
^!1 
 
 74 
 
 THIRD DEPARTMENT. 
 
 III 
 
 ^ 138. What 18 the value in American currency of 330 francs of 
 France { 
 
 139. What is the difference in value (dollars and cents) be- 
 tween 1200 crowns of Great Britain and 1200 crowns of Sweden ? 
 
 ^ 140. A New York manufacturer owes an advertising bill of 
 £•1 lis. (id. in London, England. How much will a foreign 
 money order for this sum cost him, supposing the charges to be 
 50 cents ? 
 
 141. Find the value in Swiss francs of $5.80. 
 
 142. Find the total value in American currency of the follow- 
 ing :— 
 
 Three pounds sterling. 
 
 Twenty-five shillings. 
 
 One hundred and eight pence. 
 
 Twenty-three guineas. 
 
 One hundred marks. 
 
 III. WAGES. 
 
 PRACTICAL EXERCISES. 
 
 Note. -Woffes are usually calculat-xl on a scale of ter hours' labor per day Six 
 'lays are considered one week. 
 
 143. A man earns $2.25 a day. How much will he earn in 
 a month of August the iirst day of which is Wednesday ? 
 
 144. A man earns iiK3.35 a day. How much will he earn in 
 a month of March the first day of which is Friday ? 
 
 145. A man working 11^ hours a day at 30 cents an hour will 
 earn how much in a week ? 
 
 146. How much will a boy earn in a week who earns 18 cents 
 an hour and works 12| hours a day ? 
 
 147. Thirty-five cents an hour is equivalent to how much a 
 month (four weeks) i 
 
 [< I 
 
WAGES. 
 
 76 
 
 148. A farmer hi_ed a man on March 15, at f24 a month. 
 
 The man left on November 31 following. How much did he 
 earn ? 
 
 149. A mechanic's wages are ^2.75 a day. On a certain day 
 he began work at 9.30 a.m. and left oil' at 4 p.m. How much 
 did he earn on that day if he took an hour at noon ? 
 
 160. A man earning $1.75 a day works on a certain day from 
 1 p.m. to 4.30 p.m. How much does he earn on that day ? 
 
 161. A man earning $2 a day lost 13^ hours in one week. 
 What were his wages for that week ? 
 
 162. At $2.20 a day, how much should a machinist receive for 
 142^ hours' labor ? 
 
 163. A foreman receives $2.90 a day, and 50 cents an hour for 
 overtime. During a certain week he works from'().30 a.m. until 
 10.30 p.m. (less 2 hours for meals) each day. What are his 
 wages for that week ? 
 
 154. A foreman receives $3 a day, and 60 cents an hour for 
 overtime. He is charged 20 cents for each hour he is absent. 
 His time for a week is as follows : 12 J hrs., 8 hrs., 8| hrs., 13 
 hrs,, 10^ hrs., and 13 hrs. What should his wages be ? 
 
 156. A carpenter worked a certain number of days and re- 
 ceived $41.25 ; if he had worked 21 days more he would have 
 received $67.50. How many days did he work ? 
 
 166. A boy commenced work on Tuesday, April 7, 1885, at 
 60 cents a day. He worked (six days each week) until the even- 
 ing of September 17th, 1885, except during a sickness which 
 lasted from June 27 until July 8 inclusive. Upon August 3 his 
 wages were increased to 75 cents a day. He paid $1.26 a week 
 for his board and other expenses. The rest of his money he 
 sent to his mother. How much did he send her ? 
 
 167. Three brothers, A, B, and C, worked together 12 days. 
 Their wages amounted to $63.60. C received as much per day 
 as A and B together, and B received 15 cents per day more 
 than A. Find A's dailv w^aces^ 
 
'^'^ THIRD DEPARTMENT. 
 
 DiimoTioK.-In .Mh .xeroiM which follow, find the toUl wi^e. for the week 
 
 168. Builder's Time Sheet. 
 
 T , . , . ^Z 'f"""- Wed. Thur. Fri. Sat. pe?day. 
 
 Ir^ wT • • • • ^'' 2* 5 10 10 4 $2.(i0 
 
 7'"^;"« ^ 1<> 10 10 2i 5 $2.20 
 
 Amos Pudsey . . . 9 7 10 8 10 3 $2 60 
 
 Jas. AnderBon. . . 4 10 7 9 4 4 $2.25 
 
 169. Contractor's Time Sheet. 
 
 Mon. Tue8. Wed. Thur. Fri. S.t. pe^dSy. 
 
 ^Zlr ^^ >'^^ ^^ 10 3 10 $1.75 
 
 Robt. Gilray . . . . 8^ 10 10 2h 10 10 $2.00 
 
 f ^*V:: 7 10 C 3 10 9 $1.60 
 
 ir'\v''^ ''^ ^^ ^ « 4 10 $1.40 
 
 ^^"^^V'^** 2^ 3 4 5 6 7 $1.25 
 
 Jas. Courtney. . . 8 10 10 9 7 4 $1.75 
 
 160. Manufacturer's Time Sheet. 
 
 i:l^'^'' 12 12 12 13i 6 6 $2.16 
 
 ^;^^t'' ^^ 10 10 4 5 3 $2.20 
 
 Thos. Brown.... 2 16 8 9 4| $2.00 
 
 Jauies Welch.... 5^ 6 3 10 10 10 $2.50 
 
 ^•£?,^P"^' I 10 10 9^ 12 10 $2.25 
 
 ^•^^^««" 7 9 8| 10 10 7 $2.50 
 
 161. Miller's Time Sheet. 
 
 R irn ?."■ '""''■ '''''*• '^'^"'•- '''^- Sat. pe^rdav. 
 
 ^•^^"^y 10 12 11 lOi 13 5 $1.85 
 
 i-^^*^^'^ 10 12i 7| 8 4 6 $1.15 
 
 ^- ^"e^' 10 10 10 3| 6 7 $1 40 
 
 ?-^"^« 10^ 15 Sh ^ 8 8 $1.25 
 
 '^'^^^^^ 18 »i 12 3^ 10 10 $115 
 
 HI 
 
WAGKS. 
 
 77 
 
 DiRBcnoN.-In the two exercises which follow deduct 10 cents an hour for loHt 
 time, and allow 40 cents an hour for overtime. * 
 
 162. Printer's Time Sheet. 
 
 Rate 
 
 Men. Tues. Wed. Thur. Fri. Sat. |)er day. 
 
 R- Miln 10 12 4 3^ 8 $3.00 
 
 J- Smith 8 10 5 4 12^ 5 |2.75 
 
 C.Woods 7 10 6^ 6 13 (> $2.60 
 
 W.Sim 10 7* 10 14 4 ^M 
 
 J. Mortimer . . . . 12^ 10 12 13^ 3 $2.40 
 
 E. Casweil 5 11 10 10 lo" 8 $2.25 
 
 163. FouNPRY Time Sheet. 
 
 ., .. .... _ R«t« 
 
 Mon. Tues. Wed. Thur. Fri. Sat. per day. 
 
 I^- Hood 10 8 10 14i 10 4 $2.15 
 
 K.Hall 12 9i 10 8^ 10 4 $3.10 
 
 R.Bell 12 8 10 9 10 5 $1.75 
 
 S. Root 10 8 10 10 10 4 $2.00 
 
 C. Blackhall 9 10 6 9 10 5 $2.50 
 
 Direction.— In the two exercises which follow consider eight iiours' labor a 
 full day. 
 
 164. Factory Time Sheet. 
 
 J. Seymour . , 
 T. Wyiidham, 
 S. Marshall . , 
 E. Thornton , 
 R. Ml i.well. . 
 
 Mon. Tues. 
 
 7 8 
 
 7 
 
 n 
 
 7 
 6 
 
 8 
 8 
 8 
 
 8 
 
 Wed. 
 8 
 8 
 
 8i 
 8 
 8 
 
 Thur. 
 
 n 
 
 6 
 4 
 3 
 2 
 
 Fri. 
 6 
 6 
 8 
 8^ 
 9 
 
 Rate 
 Sat. per day. 
 
 90o. 
 
 o 
 5 
 4 
 5 
 5 
 
 85c. 
 90c. 
 75c. 
 65c. 
 
 165. Cabinetmaker's Time Sheet. 
 
 Mon. 
 
 F.Allan 8 
 
 ^E. Smith 7 
 
 T. Brown 6 
 
 K. Faddis 2 
 
 J. Coulter 8 
 
 Tues. Wed. 
 
 8 8 
 
 n 
 
 7 
 
 7 
 6 
 9 
 
 >7 
 
 Thur 
 8 
 
 6 
 9 
 5 
 
 Fri. 
 8 
 
 7 
 5 
 
 n 
 
 Rate 
 
 Sat. per day. 
 
 8 $1.15 
 
 8 $1.40 
 
 6 $1.80 
 
 5 $1.75 
 
 4 fl.5a 
 
78 
 
 THIRD DEPARTMENT. 
 
 IV. BILLS AND ACCOUNTS. 
 
 HINTS AND DEFINITIONS, 
 renders.*"" '" "'"'""' " * '^'**"'*' '"**''""'* °' •"«'*^^h'»"<"«« -old, or of service. 
 
 .on\rZV!l'' "''" "'""''': ''"*^'* "'■ '^'•^'^'^•' " "'''''' <* debtor; and the per- 
 son to whom the money, goods, or services are due, is called a creditor 
 
 A 6i« should state the names of the buyer and seller, the place and time of the 
 transaction, and any special tenns agreed u,K.n by the parties. 
 
 A bin is receipted when the word- " Received Payment," or " Paid " are written 
 at the bottom, and fhe creditor, or son.e one actin/for him, affixes his name 
 
 After an itemized bill has been rendered a,.d not paid, the creditor does not 
 usually make out a second bill complete, but sin.ply the ormof rbTl wit^ the 
 
 amount. This incomplete fonn is termed a statement. 
 
 If goods a> , sold on credit after an itemized bill of a previous purchase has » n 
 rendered. th« new bill will hav^ the words "To old A'coount-T-T" Amount 
 rendered," at the top; that is. if nothing has been paid. To Account 
 
 Jyoti"" '"'" "" """""'• "' "" "''"'' "**"" *^«y *- '-t paid for when 
 BUSINESS EXERCISES. 
 
 166 
 
 Transactions. 
 
 Aug. 20, 1885. The Cue Price Store, CoUingwood. Richard 
 Ball buys <,f C. E. Brown & Co., on account, 26 yds. Silk at 
 J1.45 ; 4 yds. Lining at 15c. ; 2^ yds. Lining at 20c. ; 4 yds 
 Mushn at lie. ; 2 doz. Buttons at 25c. ; 12 yds. Flannel at 38c." 
 5 yds. Cotton at 14c.; 2 pair Kid Gloves at $1.25 ; 3A yds 
 Ribbon at 42c.; 1 Silk Handkerchief, $1.45; Gi vds Em- 
 broidery at 36c. " " 
 
 Oct. 15, 1885. Richard Ball buys of C. E. Brown & Co 
 on account, 15 yds. Black Cloth at $2.10; 5 yds. Tweed at 
 <"1.85. 
 
 Nov. 13, 1885. Richard Ball pays C. E. Brown & Co., on 
 account, cash, $45.25. 
 
 «^?oP !\T^' ^''^^'^ ^^" P*y^ ^- ^- B^°^^^ & Co. , cash. 
 ^4o. Jb to Di lance account. 
 
BILLS AND ACCOUNTS. 
 
 79 
 
 lu^Hs ATork. 
 
 lake out and render an itemized bill, Auguat 31. 
 lender a statement on September 30„ 
 
 ake oi!t the account to be rendered October 31. 
 Credit this last bill with the amount paid November 13. 
 ilender a statement on November 30. 
 Receipt this last statement in full, December 15. 
 
 Mr. Richard Ball, 
 
 [iTRMizKb Bill.) 
 
 CoLLiNowooD, Aug, SI, 18S5. 
 
 Accounts rendered monthly. 
 
 Co C. E. Brown ^ Co., ^r. 
 
 Aug. 
 
 20 
 
 ■ 
 
 26 yds. Silk ...... (cb. »1 i.'^ 
 
 37 
 
 70 
 
 
 
 
 
 4 yds. Lining . . 
 
 . @ .15 
 
 
 60 
 
 
 
 
 
 2i yds. Lining . . 
 
 . @ .20 
 
 
 50 
 
 
 
 
 
 4 yds. Muslin . . 
 
 . . @ .111 
 
 
 44 
 
 
 
 
 
 2 doz. Buttons . . 
 
 . @ .26 
 
 
 50 
 
 
 
 
 
 12 yds. Flannel . . 
 
 . @ .38 
 
 4 
 
 56 
 
 
 
 
 
 5 yds. Cotton . . 
 
 . @ .14 
 
 
 70 
 
 
 
 
 
 2 pair Kid Gloves 
 
 *. @ 1.25 
 
 2 
 
 50 
 
 
 
 
 
 3i yds. Ribbon . . . 
 
 . @ .42 
 
 I 
 
 47 
 
 
 
 
 
 1 Silk Handkerchief . 
 
 . @ 
 
 I I 
 
 45 
 
 
 
 
 
 6i yds. Embroidery 
 
 . @ .36 
 
 1 
 2 
 
 34 
 
 52 
 
 
 
 
 
 
 76 
 
 
 
 [Statkmkst.] 
 
 
 
 
 
 COLLINOWOOD, Sei 
 
 \>t. 3( 
 
 ), 1885. 
 
 Mr. Richard Ball, 
 
 
 
 S^o C. E. Broivn 
 
 & 
 
 Co., f r. 
 
 A'-nounts rendered monthly. 
 
 
 
 
 
 To Account rendered Ai 
 
 Jg. 31. . . 
 
 
 
 52 
 
 76 
 
k 
 
 ■ * 
 
 80 
 
 THIRD DEPARTMENT. 
 
 [Statbmknt and Bill.) 
 
 Colling WOOD, Oct. 31, 1S85, 
 
 Mr. Richard Ball, 
 
 ^Q C. E. Broivn ^ Cc, Dr. 
 
 Accounts rendered monthly. 
 
 Oct. 
 
 15 
 
 To Account rendered Sept. 30. . . 
 
 15 yds. Black Cloth . . @ $2.10 
 5 yds. Twee-1 , . . . © 1,85 
 
 Receivid cash, $45.25. 
 
 C. E. Bkown & Co. 
 
 31 
 9 
 
 50 
 25 
 
 62 
 
 40 
 
 93 
 
 76 
 
 :5 
 
 51 
 
 
 Mr. Richard Ball, 
 
 [Statkmknt.] 
 COLLINGWOOD, Nov. 30, 1885. 
 
 fo C. E. Broivn &> Co., )Br. 
 
 Accounts rendered monthly. 
 
 To Balance of Account . 
 
 Received payment in full. 
 
 C. E. BfvOWx & Co., 
 per B. K. 
 
 48 i26 
 
 I 
 
 NOTB.— When a clerk receipts a bill it is customary and necesaary to write his 
 initials under the name of the creditor, or to write his own name, and directly 
 underneath his own name that of his employer, preceded by the word for; as, 
 
 Received cash, $45.25. 
 
 JAMES ALLAN, 
 
 for C. E. Brown & Co. 
 
BILLS AND ACCOUNTS. 
 
 81 
 
 187 
 
 Transactions. * 
 
 March 16, 188G. The District Exchange, Jamestown, 
 Robert Walker buys of T. Myers & Co, on account, 22 lbs 
 Sugar at lie; 12 lbs. Butter at 23c.; 18 lbs. Che.se at 19c • 
 14^ lbs. Tea at 55c. ; 15^ lbs Dried Apples at be : 74 lbs. Cur- 
 rants at &c. ; 37 lbs. Biscuits at 13c. 
 
 April 2, 1886. Robert Walker pays his account in full. 
 Pupil's Work. 
 
 Rwnuer an itemized bill, March 31. 
 Receipt tlip bill in full, April 2. 
 
 168 
 
 Transactions. 
 
 April 10, 1886. Cheap Cash Store, Williamsburg. John 
 Hopkins buys of Alfred Hunt, on account, 13 yds Silk at 
 $1.95 ; 42^ yds. Sheeting at 18c. ; 32 yds. Muslin at 12Ac • 6 
 pair Kid Gloves at $1.37 ; 42 yds. Print at 9Ac. ; 22A yds. 
 iJrilling at 14c. z J' »♦ 
 
 May 12, 1886. John Hopkins pays his account in full. 
 Pupil's Work. 
 
 Render an itemized bill, April 30. 
 Receipt the bill in full, May 12. 
 
 169. 
 
 Transactions. 
 
 May 3, 1886. The Leading Grocery and Provision Store, 
 ThomaeviUe. Mar.-,hall Watson buys of C. E. Charters & Co 
 on account, 18 lbs. Sugar at 9c. ; 12 lbs. Butt.r at 28c • 31 lbs' 
 Tea at 70c. ; 8| lbs. Coffee at 34c. ; 14 lbs. Biscuits at lie • 16 
 lbs. Soap at 14c. ; 3J lbs. Cneese at 18c. ; 1| doz. Eggs at 22c 
 
 June 25, 1886. Marshall Watson pays his account in full. 
 Pupil's Work. 
 
 Render ar. itemized bill, May 31, 
 
 Receipt the bill in full, June 25. 
 
82 
 
 THIRD DEPARTMENT. 
 
 i ! 
 
 i 
 
 170. ., 
 
 Transactions. '' 
 
 January 3, 1887. The Golden Lion, Niagara. Thomas 
 Gibson nuys of .James Currie & Son, on account, 25 yds. Flan- 
 nel at 3(>c. ; 2 doz. Silk Buttons at 22c. ; 13 yds. Muslin at 14c. ; 
 16 yds. Sheeting at 18ic. ; 2 Boys' Suits, $9.50 and |12. ; 1 
 Overcoat, $13.50 ; 2 Silk Ties at 75c.; h doz. Handkerchiefs 
 at 10c. eacli ; 14| yds. Velvet at $2.40 ; 1 Fuv Cap, $2.75. 
 
 January 22, 1887. Thomas Gibson buys of .Tames Currie & 
 Son, on account, 35 yds. Tweed at $1.20 ; 14 yds. Drilling 
 at 12ic. 
 
 March 5, 1887. Thomas Gibson pays his account in full. 
 
 Pupil's Work. 
 
 Render an itemized bill, January 31, 
 Render a statement, February 28, 
 Receipt the statement in full, March 5. 
 
 171. 
 
 Transactions. 
 
 March 15, 1887. The Oak Hall Clothing Store, Topeka. 
 Mrs, J, Adair buys of T. Crompton & Co., on account, 10 yds. 
 Silk at $3.25 ; pair Hoso at 02ic. ; 2 pair Gloves at $1.35 ; 
 13i yds. Cambric at 12c.; 1 Umbrella, $3.45. 
 
 March 22, 1887. Mrs. J. Adair buys of T. Crompton & Co. , 
 on account, 6 Handkerchiefs at 27ic. ; 2 doz. Buttons at 37ic. 
 
 April 12, 1887. Mrs. J. Adair buys of T. Crompton & Co., 
 on account, 15 yds. Ribbon at 2Cc. ; 13 yds. Silk Velvet 
 at $3. 25. 
 
 June 7, 1887. Mrs. J. Adair pays her account in full. 
 
 Pupil's Work, 
 
 Render an itemized bill, March 31. 
 Render a statement and new bill, April 30. 
 Render a statement, May 31. 
 Receipt the last statement, June 7. 
 
BILLS AND ACCOUNTS. 
 
 83 
 
 172. 
 
 Transactions. 
 
 July 5, 1886. The Central Book Depot, Whitby W H 
 Huston buys of J. S. Robertson & Bros., on account, 3 quires 
 Foolscap at 27c.; 5^ quires Letter at 22c.; 1 McLellan's 
 Algebra, $1.75; 1 set Dickens, 12 vols., $22.50; 3 Ancient 
 Classics at 65c. 
 
 July 18, 188(5. W. H. Huston buys of J. S. Robertson & 
 Bros., on account, 15 Irving Library at 45c. ; (luires Foolscap 
 at 23ic. ; 1 doz. Lead Pencils at 3c. each. 
 
 August 5, 1886. W. H. Huston buys of J. S. Robertson & 
 Bros., on account, 3 Maury's Physical Geography at $1.65. 
 
 August 10, 1886. W. H. Huston pays $10 to apply on 
 account. 
 
 September 12, 1886. W. H. Huston buys of J. S. Robert- 
 son & Bros., on account, 12 Drawing Bcx.ks at 12|c. 
 
 October 14, 1886. W. H. Huston pays his account in f-Ul. 
 Pupil's Woric. 
 
 Render an itemized account, July 31. 
 Render a statement, bill, etc., August 31. 
 Render a statement and bill, September 30. 
 Receipt this last statement in full, October 14, 
 
 173 
 
 Transactions. 
 
 November 3, 1886. John Wallace buys of the Keewatip 
 Lun>borCo., oniiocount, 1350 ft. Pine at $32. 50 per M, • 0250 f: 
 Hen.iuck at $24.50 per M. ; 3650 Cedar Posts at $9.r,0 per 0. 
 
 November 15, 1886. John Wallace })uys of the Kc^r^uiin 
 Liuiiber Co. , on account, 4500 Shingles at $4. 40 per ^ '> 250 
 h « nee Pickets at $6. 80 per M. "' 
 
 December 13, 1886. John Wallace pays $122 on las account. 
 
 January 14, 1887. John Wallace p-^.ys $35 on hi. account. 
 
 February 12, 1887. John Wallace pays the balance of his 
 •iccount in full. 
 
84 
 
 THIRD DEPARTMENT. 
 
 Pupil's Work. 
 
 Render an itemized account, November 30. 
 Render a credit statement, December 31. 
 Render a credit statement, January 31. 
 Receipt this last statement in full, FebrJiary 12. 
 
 174. 
 
 Exercise 1G7. — Robert Walker encloses the amount of his 
 account in a letter to T. Myers & Co. Write the letter. Date, 
 April 2. 
 
 Exercise 109.— Pupil, as C. E. Charters & Go's clerk. Write 
 a short note to Marshall Wats<m, requesting a settlement of his 
 account. Date, June 20. 
 
 Exercise 170. — Write a short note at the bottom of the state- 
 ment of February 28, recjuesting payment. 
 
 Exercise 172. — Pupil, as W. H. Huston. Write a letter to 
 J. S. Robertson & Bros. , ordering the books, etc., named in the 
 transaction of Jtily 5. 
 
 Exercise 172. — Pupil, as J. S. Robertson & Bros' clerk. 
 Answer the letter received from W. H ton, July 5. 
 
 Exercise 173, — Write a letter to Wallace, enclosintj 
 
 statement of his account, and ruquesm.^ ai immediate settle- 
 ment. Date, February 10. 
 
 V. REVIEW. 
 LOSS AND GAIN EXERCISES. 
 
 175. A lumber dealer bought 32,450 feet of lumber at $22 per 
 M., and sold 11,750 feet at $34 per M., and the remainder at 
 $28 per M. How much did he gain ? 
 
 176. A grocer bought 100 loads of potatoes, of 30 bushels 
 each, at 37| cents a bushel. Allowing 7^ bushels for waste, how 
 much will he gain by retailing the rest at 16 cents a peck ? 
 
 il 
 
REVIEW. 
 
 85 
 
 177. A milk dealer buys 27 ten-gallon cans of milk each day 
 at $1.75 a can. He keeps three delivery wagons at an expense 
 of $1.75 each a day, and sells the milk at 7 cents a quart. Find 
 his gain in ten weeks, including Sundays. 
 
 178. A fruit dealer bought 5 barrels of apples at $2.75 a barrel. 
 The 5 barrels cc.ntained 4950 apples. He sold them at the rate 
 of 7 for 5 cents. How much did he gain ? 
 
 179. A farmer bought 13 head of young cattle for $215. He 
 kept them for six months at an expense of $3 a head per month, 
 and then sold them at $32 each. Did he gain or lose, and how 
 much ? 
 
 180. Three brothers chopped wood during 20 weeks of a cer- 
 tain winter. They averaged 7 cords a day. Their board cost 
 $2.50 a week each. They sold the wood at $1.75 a cord. How 
 much did each make '! 
 
 181. A man bought a house and lot for $7842. He built an 
 addition to the house at a cost of $1643. The house was destroyed 
 by fire, and he received insurance $3520. He then sold the lot 
 for $5215. How much did he lose ? 
 
 182. A well digger agreed to dig a well upon the following 
 terms : 40 cents for the first foot, 45 cents for the second, 50 
 cents for the third, 55 cents for the fourth, and so on to Lny 
 depth. He paid a man $1 a day to assist him. If it took him 
 .six days to dig the well 22 feet deep, and he paid 40 cents a day 
 for board, how much did he make !? 
 
 183. A merchant had goods on hand January 1, 1885, valued at 
 $12,324. He bought goods at a cost of $7623, and sold goods to 
 the amount of $14,265 during the year. On December 31, 1885. 
 his stock book showed goods on hand valued at $8937. How 
 much did he gain during the year ! 
 
 184. Two farmers hired a steam thraslier for six months at 
 '1*22 a lUf.Dth. They were employed during 127 days of that time, 
 and their expenses were $3.25 a day. They thrashed ($3,246 
 bushels of grain, f(,r which they received 3^ cents a bushel. 
 H(.w much did they make during the six months ? 
 
 
86 
 
 THIRD DEPARTMENT. 
 
 ) I ,1 
 
 ! '1 
 
 ,,J* • 
 
 _i 
 
 M 
 
 MISCELLANEOUS EXERCISES. 
 ^ 185. Find tlie cost of !M)0() aliuets of paper at ^.20 a ream. 
 
 186. How many hours from 10.15 a.m., Tuesday, until 7.45 
 p.m., Sunday? 
 
 187. ^>i>o peck of clover seed will sow an acre. What will it 
 cost to sow 8 acres, if the seed costs 11 cents a pound ? 
 
 188. A train passes a telegraph pole every 4 seconds. If the 
 poles are (U) yards apart, how many miles an hour is the train 
 going '{ 
 
 189. At 5 cents a quart, how much will a bushel of chestnuts 
 cost ? 
 
 190. If a man's income is 5 cents a minute, what will be his 
 "i total income during the three summer months { 
 
 191. A schoolbt)y is 5 minutes late evyry day. How much 
 I'time does he lose in 112 days ? 
 
 192. A clock was 15 mi)u>tes fast at 11.30 a.m. on Monday. 
 It lost time gradually, and was 10 minutes slow at 3.15 p.m. on 
 Tuesday. At what time van it exactly right ? 
 
 193. A race course measures 1 fur. 8 rods 2 yds. 2 ft. How 
 often must one go around it to travel 5 miles ? 
 
 194. How many reams of paper are there in an edition of 6000 
 copies of a book of 1()0 pages, each sheet of the i)aper l>eing 
 folded four times 1 
 
 \ 
 
 195. A dealer bought 5 gross of steel pens at $1.50 a gross, 
 and sold them at 15 cents a dozen. How much did he gain ? 
 
 196. If <»ne quart of nuts cost 11 cents, how many bushels can 
 be bought for $13. 20/ 
 
 197. A clock which gains 15 minutes in every 15 hours is right 
 at noon on Monday. When will it again be right ? 
 
 198. How much did I gain on 40 bushels of berries, bought at 
 $4 a bushel, and sold at 15 cents a (]uart !* 
 
REVIEW. 
 
 87 
 
 199. Find the value of tlie rails in a straight fence 40 rods 
 long, each rail being 11 feet long, and the fence G rails high, at 
 *22.50perM. 
 
 200. A stationer buys 3 gross of lead i)encils at ^.75 a gross, 
 and retails them at 7 cents each. How much does he gain on 
 the lot i 
 
 201. Find the cost of 2(;,30() pounds of hay at ^14.50 a ton. 
 
 202. Water exi)and8 ^ in freezing, and one cubic foot of 
 water weighs 1000 ounces. Find the weight in tons of the ice 9 
 inches deep formed on a pond liaving an area of 3 acres. 
 
 203. There are 50 jjupils in a room 3G feet long, 30 feet wide, 
 and 16 feet high. How many cubic yards of air are tliere for 
 each pupil ? 
 
 204. How many half-pint bottles can be filled from a ten- 
 gallon can of milk ! 
 
 206. A man was born February 29, 1824, and died March 18, 
 1885. How many birthdays had he '( 
 
 206. A horse reijuires three gallons of oats a day. When oats 
 are worth 50 cents a bushel what will it cost to feed him during 
 the months of December and Januaiy ? 
 
 207. Show that if the price in pounds of laying a mile of raila 
 be multiplied by 2 and divided b> 11 the result is the price in 
 farthings of laying a foot of rails. 
 
 208. How many bullets, each weighing i oz., can be moulded 
 fi'om 2 pounds 4 ounces of lead 'I 
 
 209. A man bought 34,750 pounds of hay at $15 a ton, and 
 sold the same at 85 cents a hundredweight. How much did he 
 gain ? 
 
 210. If one bushel of wheat makes 40 pounds of flour, how 
 many barrels of flour, containing 19G pounds each, ought a grain 
 merchant to receive from 4263 bushels of wheat ? 
 
 211. A drover bought 29 head of cattle for f928, and sold them 
 for $1015. How much did he gain on each ? 
 
«i' i 
 
 88 
 
 THIRD DEPARTMENT. 
 
 212. The wages of 20 men for 4 days is $84. What is a man's 
 daily wages ? 
 
 213. Divide $1970 among 15 persons, giving to four of them a 
 double portion. 
 
 214. Twenty men can do a piece of work in 40 days. If 5 
 men assist them how long will it take ? 
 
 215. A company of 45 men have victuals for 30 days. How 
 many men must leave that the provisions may last 50 days ? 
 
 216. Two trains start at the sarae time and place, and go in 
 the same direction ; the first goes 35 and the second 28 miles 
 an hour. At the end of 25 hours the first begins to go in the 
 opposite direction. In how many hours from the time of start- 
 ing will they meet ? 
 
 217. A man who can row 4 miles an hour in still water can 
 row 2 miles down stream in 20 minutes. How long will it take 
 him to row 2 miles uj) stream ? 
 
 218. How many times can a vessel containing 3i quarts be 
 filled from a barrel containing 105 gallons ? 
 
 219. What number is that to which if | of itself be added the 
 sum will equal 77 ? 
 
 220. The H. C. F. of two numbers is 39, and their L. C. M. 
 is 190905. One of the numbers is 2145 ; find the other. 
 
 221. Find the cost of 298,400 shingles at $4.80 per M. 
 
 222. How many thirty-inch steps will a soldier take in march- 
 ing 6^ miles ? 
 
 223. Find the value of 427 pounds of oat meal at 47 cents 3 
 stone. 
 
 224. A man has 2568 English crowns. How many Danish 
 coins of the same name should he receive for them ? 
 
 225. A horse and carriage are valued at $350 ; ^ of the value 
 of the horse is equsil to | of the value of the carriage ; find the 
 value of each. 
 
REVIEW. 
 
 89 
 
 ^ 
 
 226. If 58. be equal to ^1.22, find the value of £3 148. 6d. in 
 American currency. 
 
 227. The numerators of two fractions are 6 and 11, and ^ the 
 sum of the fractions is equal to J of ^. What are the fractions ? 
 
 228. Find the value of 21 baskets of strawberries, each con- 
 taining 14 (quarts, at 12A cents a quart. 
 
 229. Find tlie value of 3 dressed hogs, weighing respectively 
 289h pounds, 211^ pounds, and 234 pounds, at 1^7.25 a hundred- 
 weight. 
 
 230. A boat moves 17 feet 6 inches at each stroke. How far 
 in miles will it move in 12,000 strokes ? 
 
 231. How many days of 12 hours each will a man take to 
 count a million gold dollars at the rate of 80 a minute ? 
 
 232. if a grocer use a 15 ounce instead of a pound weight, 
 how much does he cheat a customer who buys what he supposes 
 to be 12 pounds of tea at 75 cents a pound ? 
 
 233. How much must be paid in Canada for 85 hundredweight 
 of oats at 75 cents a bushel ! 
 
 U ^^' ^^ ^ square miles of land be equally divided among 48 
 -^ settlers, how many acres will each have ? 
 
 236. How many carats fine is a ring which is composed of f 
 pure gold ? 
 
 236. A bought apples at the rate of G for 5 cents, and B bought 
 oranges at the rate of 3 for 4 cents. How many oranges should 
 B give A for 48 apples ? 
 
 237. If you buy a pound of tea at 65 cents, 3 dozen eggs at 
 13 cents, 2 pounds of soda at 11 cents, 7 yards of ribbon at 24 
 cents, and a hat at $1.25, and the merchant throws off 10 cents 
 from every dollar's worth bought, how much change should you 
 get out of a $5 bill ? 
 
 238. There are two numbers whose difference is 245, and 
 whose sum is 965 ; find their product. 
 
90 
 
 THIRD DEPARTMENT. 
 
 239. If telegraph poles coat 25 cents each, and wire | of a cent 
 a yard, how much will the material coat for 3 miles of telegraph 
 line, consisting of 3 wires, the poles being ()() yards apart ? 
 
 240. A locouKjtive burns a ton of coal while going 75 miles, 
 and moves forward 10 yards every time the driving wheels turn 
 round. How many times does the driving wheel revolve for 
 every pound of coal burned ? 
 
 241. Wheat has been bought at 85 cents a bushel. At what 
 price per cental must it be sold so that after paying freight 
 charges of 8 cents a bushel the gain may be 1 of the entire cost ( 
 
 242. A grain merchant ahipi)ed 8500 bushels of barley at a 
 cost of ('} cents a bushel ; he sold it at 75 cents, and gained ^40 
 on the lot. How much did he pay f<jr each bushel ? 
 
 243. There are 3(i men employed on a job, all receiving the 
 same wages ; at the end of 42 days they receive ^402. What 
 does each man receive per day ? 
 
 244. In what time will a boy, at 76 cents a day, earn as much 
 as a man earns in 00 days at $2.75 a day I 
 
 245. A number of cattle that cost »07!>2 were sold for .^12,090, 
 by which a profit of $12 a head was made. How many head of 
 cattle were there ? 
 
 246. Find the cost of 9840 cedar rails at $3.25 a hundred. 
 
 247. When a train is moving at the rate of 24 miles an hour, 
 how long will it take it to i)ass 24 telegraph poles, the distance 
 between the poles being GO yards ? 
 
 248. A merchant pays $8.90 for butter at 24 cents a ]>ound, 
 but in buying, uses a weight of 1G| ounces instead of a pound. 
 In selling he uses a weight ^ of an ounce less than a pound. 
 How much dishonest profit does he make by retailing the butter 
 at 27 cents a pound ? 
 
 249. A drover bought 247 sheep at $4.75 each, and 42 more at 
 $4.40 each. Eight of them died, and he sold the rest at $0 each. 
 How much did he gain ? 
 
FOURTH DEPARTMENT. 
 
 I. SURFACE MFASUREMENT. 
 
 HINTS AND DEFINITIONS. 
 
 *7 A surface how length and breadth without thickness, 
 
 A rectangle U a plane figure hounded by four straight lines, and having four 
 rifrht angles. 
 
 V rectangle is called a square when all its sides are cfiual. 
 
 The area of a rectangle is expressed by the product of the length and the 
 breadth. 
 
 Before multiplying, it is necessary that both dimensions be expressed in units of 
 the same denomination. 
 
 A triangle is a plane figure bounded by three straight lines. 
 
 The United States and Canadian public lands are divided, by lines running 
 north and south, accordlnff to the true meridian, and by others crossing them at 
 right angles, into townships six miles square. 
 
 Townships are sub-divided into sections, containing «40 acres, or one square 
 mile each. 
 
 Sections are subdivided into half-Hectiom, quarter-sections and Imlf-quarter- 
 sections. 
 
 PRACTICAL EXERCISES. 
 
 ^ 1. How luauy 8(iuare iuclies in the surface of a table 9 feet 
 
 by 4^ feet ? 
 
 2. How many square yards in a blackboard 32 feet long by 
 4^ feet wide ? 
 
 3. How many square rods in a garden 231 feet long by 165 
 X feet wide ? 
 
 4. Find the cost of a piece of oil cloth 24 feet long by 15 feet 
 y 9 inches wide at 85 cents a square yard. 
 
 5. What will it cost to cement a cellar bottom 36 feet long by 
 23 feet 7 inches wide at 96 cents a square yard ? 
 
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 WEBSTER, N.Y. 14i80 
 
 (716) 872-4503 
 
 
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92 
 
 FOURTH DEPARTMENT. 
 
 A 
 
 8. Find the cost of painting a i lackboard 23 feet long by 2 
 feet 3 inches wide at 48 cents a square yard. 
 
 7. What was the total cost of paving a street 1 mile long and 
 1^ chains wide at 45 cents a square foot ? 
 
 8. A rectangular garden is 48 yards long by 48 feet wide • 
 what is its area in square yards ? ' 
 
 9. How many yards of satin, | yard wide, will it take to line 
 22^ yards of velvet ^ yard wide ? 
 
 10. A certain city is 5 miles square. Its population is 211,200 
 How many square feet of land are there to each person ? 
 
 DIRECTION -The dimensions of rectangular pieces of i^round are given, and the 
 area of each in acres is to be found. 
 
 g 11. 36 rods by 40 rods. 
 
 12. 26 rods by 60 rods. 
 
 13. 80 rods by 36 rods. 
 
 14. 16 rods by 10 rods. 
 
 15. 48 rods by 50 rods. 
 
 Q 21. 24 chains by 10 chains. 
 
 22. 36 chains by 25 chains. 
 
 23. 96 chains by 55 chains. 
 
 24. 50 chains by 49 chains. 
 26. 39 chains by 70 chains. 
 
 26. 75 chains by 96 chains. 
 
 27. 25 chains by 19 chains. 
 
 28. 27 chains by 65 chains. 
 
 29. 63 chains by 35 ch£ ins. 
 
 30. 48 chains by 95 chains. 
 
 lb 
 
 16. 75 rods by 32 rods. 
 
 17. 84 rods by 20 rods. 
 
 18. 96 rods by 60 rods. 
 
 19. 38 rods by 80 rods. 
 
 20. 70 rods by 96 rods. 
 
 31. 28 rods by 10 chains. 
 
 32. 32 rods by 15 chains. 
 
 33. 64 rods by 25 chains. 
 
 34. 40 rods by 36 chains. 
 36. 50 rods by 48 chains. 
 
 36. 96 rods by 240 chains. 
 
 37. 215 rods by 50 chains. 
 
 38. 240 rods by 96 chains. 
 
 39. 144 rods by 100 chains. 
 
 40. 100 rode by 144 chains. 
 
SURFACE MEASUREMENT. 
 
 93 
 
 ^ • o.^/' ^""^ "^""^^ ^"^""^ y*""**" """^ *^«''« ^» *l^e ^alls of a room 
 24 feet long, 15 feet wide, and 14 feet high ? 
 
 42. If a rectangular field which contains 16 acreB is 40 rods 
 wide, how long is it ? 
 
 43. A field containing 18 acres is 80 rods long. Find the cost 
 of fencing it at $1.25 a rod. 
 
 44. A rectangular field containing 27 acres is 30 rods wide 
 What will It cost to fence it at 5 cents a yard ? 
 
 46. The perimeter of a rectangle is 400 feet, The diflference 
 between the length and breadth is 40 feef . fL the ^eL 
 
 J 46. How many acres of land in a half-quarter-section ? 
 
 ■f land''? ^^** ^""^ *^^ dimensions in rods of a quarter-section of 
 
 ^~ f '^' r^l*^*" ""^^"^ ""^ * township of land at the rate of $120 
 for each half-section. 
 
 ^ 1 49. How many quarter-sections in a piece of land 16 miles 
 long by 4 miles wide ? 
 
 y 50. What is the value of the land in a piece of country 42 
 ' miles square at $1.50 an acre? 
 
 II. SOLID MEASUREMENT. 
 
 HINTS AND DEFINITIONS. 
 A solid has length, i , eadth, and thickness, or height 
 A rectangular solid is a body bounded by six rectangular surfaces 
 If all the surfaces or faces of a rectangular solid are equal, it is caUed a cube 
 
 brellTSti^M.'"*'^"'^"'''' ""' '' '''''''''' '^- ''^ P^^-* o' *»>« '-^i'^. 
 ^^The three given dimensions must be expressed in the units of the same denomi- 
 
 A cubic yard of earth is called a load. 
 
 The standard cordwood pile is 8 feet long, 4 feet high, and 4 feet wide ana 
 hence contains 8 x 4 x 4, or 128 cubic feet. K . na 4 leet wide, and 
 
mm 
 
 94 
 
 FOURTH DEPARTMENT. 
 
 PRACTICAL EXERCISES. 
 
 61. How many cubic inches in a cube, one edge of which is 3. 
 feet I 
 
 52. What is the volume of a solid 6 fe«t 4 inches long, 4 feet 
 6 inches wide, and 8 feet high ?, 
 
 53. How niany cubic yards of earth must be removed in dig- 
 ging a cellar 12 feet long, 10 feet wide, and 5| feet deep ? 
 
 54. A room is 25 feet long, 24 feet wide, and 18 feet inches 
 high. How many cubic feet of air does it contain ? 
 
 55. What will it cost to dig a cellar 60 feet long, 48 feet wide, 
 and 7 feet 4 inches deep, at GO cents a load ? 
 
 56. If a block of soap 3 inches long, 2 inches wide, and li 
 inches thick weighs 8 ounces, what will be the weight in pounds 
 of a cubical block of soap, each dimension of which is 3 feet ? 
 
 57. How many cubic inches in 3 cords of wood ? 
 
 58. How many cubic-inch blocks will it take to fill a mortise 
 14 inches long, 3 inches vdde, a.:d 6 inches deep ? 
 
 59. How many cubic feet in a biccV of stone 15 feet long, 13 
 feet wide, and 14 feet thick ? 
 
 60. How many cords of wood in a pile 12 feet long, 12 feet 
 high, and 8 feet wide ? 
 
 61. Find the value of a pile of tan-bark 120 feet long, 44 feet 
 wide, and 16 feet high, at $2.25 a cord. 
 
 62. Find the value of a pile of wood 242 feet long, 28 feet 
 wide, and 12 feet high, at $3.75 a cord. 
 
 63. A sleigh upon which four-foot wood is piled is 10 feet lopg. 
 How high should the wood be piled to make two cords ? 
 
 64. What should be the length of a cord of five-foot wood, 4 
 feet high ? 
 
 65. What should be the length of a cord of three-foot wood, 6 
 feet high ? 4 feet high ? 
 
LUMBER MEASUREMENT. 
 
 95 
 
 88. A cord of 2^-foot wood is 6 feet long ; how high it it?; 
 
 vy^ 87. Find the cost of a block of marble 6^ feet long, 3 feet wide, 
 and 2 feet 3 inches thick, at ^2.25 a cubic foot ? 
 
 t^ 88. How many cut sto.ies, each 8 inches by 4 inches by 5 
 inches, will it take to construct a wall one-half a mile long, 10 
 feet thick, and 27 feet high ? 
 
 89. How many cords of wood can be piled into a woodshed 20 
 feet long, 18 feet wide, and 16 feet high ? 
 
 Note.- A cubic foot of water weighs 1000 ounces. -^ 
 
 yC 70. What weight of water will a rectangular cistern contain, 
 the length being 5 feet, the breadth 3^ feet, and tlie depth 12 
 feet? 
 
 III. LUMBER MEASUREMENT. 
 
 HINTS AND DEFINITIONS. 
 
 Lumber, as the term is used here, includes boards, plank, scantling, joists, and 
 sawed timber. 
 
 A board foot is the unit of measurement. It is one foot long, one foot wide, 
 and one inch thick. 
 
 .\1I lumber less than one inch in thickness is considered inch lumber in 
 measuring. 
 
 To find the number of board feet, or feet of lumber in a board or plank, multiply 
 the length in feet bif the loidth and thicknesa in inches, and' divide the product 
 
 by 13. 
 
 PRACTICAL EXERCISES. 
 
 71. Find the number of board feet in a board — 
 
 1. 12 feet long, 12 inches wide, 1 inch thick. 
 
 2. 12 feet long, 10 inches wide, 1 inch thick. 
 
 3. 13 feet long, 18 inches wide, 1 inch thick. 
 
 4. 14 feet long, 7 inches wide, 1 inch thick. 
 
 72. Find the number of board feet in a plank — 
 
 1. 12 feet long, 18 inches wide, 1| inches thick. 
 
 2. 12 feet long, 14 inches wide, 1^ inches thick. 
 
 3. 13 feet long, 16 inches wide, 1| inches thick. 
 
 4. 16 feet hmg, 13 inches wide, If inches thick. 
 
96 
 
 FOURTH J^EPARTMENT. 
 
 ii 
 
 73. Find the number of board feet in a plank- 
 
 1. 19 feet long, 12^ inches wide, 2 inches tluck. 
 ^. 18 feet .ong, 13^ inches wide, 3 inches thick. 
 
 3. 16 fee ong, 14^ inches wide, 2 inches thick. 
 
 4. 10 feet long, 15* inches wide, 2 inches tluck. 
 74. Find the number of board feet in a plank- 
 
 1. lll^^yong, 18 inches wide, 2^ indies thick. 
 ^. 8^ feet ong, 10 inches wide, 3^ mches thick 
 ^. 7 feet or.g, 15 inches wide, 2^ inches thick. 
 4. 9 feet long, 9 inches wide, 3^ inches thick. 
 76. Find the number of board feet in a scantling- 
 
 1. 10 feet long, 3 inches wide, 2^ inches thick. 
 
 2. 14 feet ong, 4 inches wide, 3^ inches thick. 
 
 7 in rl ^"^' ^ ^"'^'' ^^^^' ^i ^"«hes thick. 
 4. 20 f -et long, 5 inches wide, 3| inches thick. 
 
 76. At $18 per thousand find the total cost of 
 
 2 boards 12 feet long, 2 feet wide, 1 inch thick. 
 
 ! iTf ]t r' ^^' ^^''''' "^^^' 1^ -«hes thick. 
 
 4 bc5ards 15 feet long, 2^ feet wide, 1^ inches thick. 
 
 77. At $20 per thousand find the total cost of 
 
 5 planks 18 eet ong. 15 inches wide, 3 inches thick. 
 7 planks 8 feet long, 12 inches wide, 2 inches thick! 
 
 78. At r-7.50 per thousand find the total cost of 
 
 b .cantlings 18 feet long, 4 inches wide, 3 inches thick 
 9 scanthngs 14 feet long, 5 inches wide 4 inches th Lk 
 8 scantlings 12 feet long, inches wide,' 5 inches thLk" 
 
 and'l8 tleTs'^Ltl ^' ^""^'^^ ^" ^ ''''' ^' '"^'^ '^ ^^ ^ong 
 anLtZTuall '' ^"'"'^^ ^" ^ ''''' ^' ^^'"^^ ^^ ^^t long 
 
LUMBER MEASUREMENT. 
 
 97 
 
 >. 
 
 ..J 
 
 V 
 
 /^ 
 
 fi f!!; ^7 ""T. f^'* "- '"'"^'' ^" ^ "*^«^'^^ 100 yardB long, 
 
 6 feet wide, and 1^ inches thick ? ** 
 
 83. How many feet of lumber in a board fence 40 rods lone 
 6 feet high, and 1 inch thick ? **' 
 
 th^usand"^ ^^^ *''''*' "^ ^^*^ ^^'^^^ ""^ ^"'"^^'' ''^ *^^'^0 per 
 
 thoLnd"'^ ^''^ '""'^ ""^ ^^^^ ^^^^^ "^ ^""""""^ ^^ *^-25 per 
 
 86. Find the cost of 12 planks each 12 feet long, 12 inches 
 wide, and 3 inches thick, at $12 per thousand. 
 
 i^f; f ''^/'*' '^^^^ °^ ^^J^^ l»'»^er for a platform 220 feet long, 
 132 feet wide, and 2 inches thick, at $24 per thousand. 
 
 88. How many board feet in a plank 14 feet long, 12 inches 
 wide, and ?l inches thick ? ^ 
 
 89. What is the cost of 468 fence boards 16 feet long and 9 
 inches wide, at $16 per thousand. 
 
 90. At $22 per thousand find the cost of the lumber required 
 to enclose a square ten-acre field with a board fence ; the boards 
 to uo 11 feet long, 6 inches wide, and 1 nich thick, and the fence 
 tour boards high. 
 
 91 How much inch lumber will be required to cover a walk 
 4 feet wide around a rectangular garden 300 yards by 250 yards ? 
 
 92. Find the cost of 26,340 feet of lumber at $27 50 oer 
 thousand. -»- •• ^^ poi 
 
 J\ t^^'^r ^f ^^'^' ^""^ ^"^ 1^ ^^«* ^'^^ i« covered with 
 plank 2i inches thick. Find the value of the plank at $18 50 
 per thousand. -r . v 
 
 94. Fin J the cost of 3 boards, each | of an inch thick, 18 feet 
 long, and 14 inches wide, at $24 per thousand. 
 
 95. A plank sidewalk 18 feet wide and 2 inches thick is to be 
 cosir at $18 per thousand i 
 
 G 
 
 I 
 
98 
 
 FOURTH DEPARTMENT. 
 
 mi 
 
 /, 
 
 X 
 
 IV. BUILDING AND FURNISHING. 
 
 HINTS AND DEFINITIONS. 
 
 Excavations are estimated by the cubic yard. 
 
 Brickwork i^ usually estimated by the thousand bricks. 
 
 The dimensions of an ordinary brick are 8 inches by 4 Jnches by 2 inches. 
 
 For ordinary calculation it is sufficiently accui-ate to reckon 27 bricks to the , 
 cubic foot, laid dry, or 20 bricks laid in mortar. 
 
 Stonework is usually estimated by the perch, containing 24} cubic feet. 
 
 In fstimatinu material, allowance is made for doors, windows, and corners. In 
 estlmatinif the work, the measure is usually taken on the outside of the walls. 
 
 To find the number of perches in a wall, divide the contents in cubic fett by 24J. 
 
 To find the number of common bricks in a wall, multiply the contents in cubic 
 feet by 20. 
 
 Plastering and painting are estimated by the square yard. 
 
 Carpet l« usually either 27 inches or 86 inches wide. 
 
 PRACTICAL EXERCISES. 
 
 96. Find the coat of excavating a cellar 20 feet square and (i 
 feet deep at 90 cents a cubic yard. 
 
 97. What will it cost to build a stone wall 990 feet long, 3 
 feet wide, and 12 feet high, at $7.50 a perch ? 
 
 98. How many perches of masonry in a wall 9 feet high and 
 2 feet thick, enclosing a garden 13 rods long and 9 rods vide 
 (outside measurement)? 
 
 99. How many bricks will be retpiired to build a wall 224 feet 
 long, 12 feet high, and 1 foot 6 inches thick? 
 
 100. What will it cost to plaster a room 32 feet long, 18 feet 
 wide, and 13 feet high, at 12 cents a square yard, allowing 2U0 
 square feet for doors and windows ? 
 
 101. How many yards of carpet, 27 inches wide, will be re- 
 quired for a hall 11 feet 3 inches wide and 64 feet long? 
 
 102. A pile of ordinary bricks is 8 feet 6 inches high, 14 feet 
 long, and 15 feet wide. What is the pile" worth at $12.50 a 
 thousand? 
 
BUILDING AND FURNISH fNO. 
 
 3t high and 
 
 99 
 
 103. How many yards of wall paper 2 feet ^de will b7r7- 
 quired for the sides of a hall 72 feet long and 14 feet iTigh? 
 
 Ju2ofjf "-ny bricks laid in mortar will be required for a 
 wall 120 feet long, 18 feet high, and 2 feet thick / 
 
 «22?peth'"" "'" ""'""' ''^' ^"'^^ ''''-' «»^ ^^--^ at 
 
 «18^0 ;^ ^J''' wall contains 2970 cubic feet; find its cost at 
 «1H.50 per thousand bricks. 
 
 ch,r°ch I'"/ l\" '^'* "^ ^^^^^'"""^ ^^«^a"« -»d ceiling of a 
 chu.ch G4 feet long, 48 feet wide, and 21 feet high, at 17 cents 
 H yard, allowmg 900 square feet for doors and windo;s 
 
 petTt'stlol" ^f '"' '^ !' '''' " ''^^P^'^^ "i*^ 3«--J> -r- 
 
 at 75 .1; ^"1 ' ^"!'^r"^^'^ ^^ ' ''"'i''' ^^'^'^ «»e foot wide 
 at 75 cents a yard. Find the total cost. 
 
 109 Two strips of moulding at 12^ cents a foot are placed 
 around a drawing room 24 feet by 16 feet. Find the cost ? 
 
 110. The floor walls and ceiling of a room 18 feet long 10 
 eet wide, and 12^ feet high, are made of inlaid walnut, oak^'and 
 
 labor, and $7o a thousand for lumber, surface measurement. 
 
 111. Ho^v many shingles, laid 4 inches to the weather, will be 
 
 TdToo f^t tT '' ' '^^" ''-' '''' '' ^'''' '' '' '-' ^'^'^ 
 
 112. If one thousand laths cover 70 yards of surface, and 11 
 pom,ds of lath nails nail them on, what will it cost to lath the 
 walls and cedmg of a school house 42 feet long, 30 f.et wide 
 and 14 feet high, at $2 a thousand for laths, cents a pound t; 
 nails, and 3^ cents a yard for lab<.r ? 
 
 113. Find the cost of a piece of oil cloth 22A feet by 17A feet 
 at 63 cents a square yard. ^ 
 
 I Jl. f \^f'. V'''^ "^'^ ^t cost to carpet a room 15 feet 9 inches by 12 
 1-7- teet 6 mches with carpet 27 inches wide at $1.50 a yard? 
 
100 
 
 FOURTH DEPARTMENT. 
 
 V. THE METRIC SYSTEM. 
 
 HINT8 AND DEFINITIONS. 
 
 The m«trlc system is a system of wol(?htg and measures based upon tne 
 decimal notation. 
 
 The unit o( measure for lens:t,h is a meter ; and from this are derived the units 
 of surface, volume, and weight. 
 
 The Standard meter is the length of a bar of very hard met*l, carefully pre- 
 served at Paris. It is about 39.37 Inches in length. 
 
 The principal units of measure are, the meter for lengths, the square meter 
 for surfaces, the cubic meter for large volumes, the liter for similler volumes, 
 and the gram for weights. 
 
 Linear Mrasurk:— 
 
 A millimeter 
 A centimeter 
 
 A meter 
 
 A kilometer 
 
 .001 of a meter. 
 .01 of a meter. 
 
 Principal unit. 
 
 1000 meters. 
 
 Mkahiirkb ok Sl'RKace:— 
 
 A s<iuare centimeter = .OOOi of a square meter. 
 
 A square meter Principal unit. 
 
 A square dekameter = 100 square meters. 
 
 A squa.e kilometer = 1,003,0)0 square meters. 
 
 MKAHURBS of VoiiUMB :— 
 
 A cubic centimeter 
 
 A cubic decimeter 
 
 A cubic meter 
 
 =t .000001 of a cubic meter. 
 = .001 of a cubic meter. 
 
 Principal unit. 
 
 Measures ok Weight :— 
 
 A milligram = .001 of a gram. 
 
 A gram Principal imlt. 
 
 A kilogram = 1000 grams. 
 A metric ton = 1000 kilograms. 
 
 In the measurement of land, a square dekameter is called an are. One hundred 
 ares = one hectare, which is enual to about 2.47 acres. 
 In measuring wood the cubic meter is called a ster. 
 In measuring liquids, grain, etc., the CUblC decimeter is always called a liter. 
 
 A cubic centimeter of water weighs a en^am. 
 
 A liter of water weighs a kilogram. 
 
 A cubic meter of water weighs a metric ton, 
 
 'WoTB. — To completo the above tables several other denominations should be 
 added, but as these are rarely used they.have been omitted. 
 
THE METBIC SYSTEM. 
 
 101 
 
 One hundred 
 
 lalled a liter. 
 
 >n8 should be 
 
 PRAC3TIOAL EXERCISES. 
 
 116. How many centimeters in 3 kilometers? 
 
 117. How many grams in a metric ton? 
 
 me^tef? ^^''^ '' *^' ''"^"' ""^ ^® centimeters of doth at $5.20 a 
 
 119. A train runs 288 kilometers in 9 houro, how n.any 
 meters does it run in a minute ? ^ 
 
 120. How many square meters in 12 ares? 
 
 121. How many cubic centimeters in .016 cubic meters? 
 
 122. How many liters in 3.7 cubic meters ? 
 
 ^m. Give the weight in kilograms of .3243 cubic meters of 
 
 \fi meters wide, 
 'kS a ster, 
 
 e length is 7 
 
 126. A pile of wood is 3. 5 kilon ' 
 and 320 centimeters high. Fiid its 
 
 126. Find the area of the walls of 
 meters, breadth 5.2 meters, and height 4 m... 
 
 H nin!" ^r ™^7 '"^''' "'"*""' ^^ * b^^«^ 9 centimeters long 
 S centimeters wide, and 7 centimeters deep ? ^' 
 
 r2f\u^ "'^'^ ^"^' * *''" ^"'^^"*^>> '^^ potatoes for 1(^24, and 
 retails them at 5 cents a kilogram. What profit does he make? 
 
 129. What is the weight of water required to fill a vat 90 
 ^centimeters long, 64 centimete,. wide, and 36 centimeters deep? 
 
 ouWc^;,«t ^'^7 '^ ^^ '"''^^' ^-^^^ ^'^''''- How much does a 
 <!Ubic meter of air weigh? 
 
 the!L"omrr' i' ??•// ""^"^ '""«• ■""" height ,«u,t 
 TOe swes of the ster be to hold a cubic meter » 
 
102 
 
 FOURTH DEPARTMENT. 
 
 138. VVJmt is the value of a kilometer of silk at $1.76 ,a 
 meter? 
 
 133. In 63 area how many 8(iuare meters i 
 
 134. How many wiuare meters in a building lot meters by 
 28 meters? 
 
 135. How many cubic meters in a box 4.7 meters by 6.G 
 meters by 7.3 meters? 
 
 136. A pile of wood containing 432 sters is 2.5 meters liigli 
 and two meters wide. How long ia it? 
 
 137. How many liters in a vessel whose capacity is 3 cubic 
 meters ? 
 
 139. What is the weight in grams of 6 cubic meters of water? 
 
 139. Find the value of the gold leaf, at 3 cents a square centi- 
 meter, required to cover the surface of a cubic decimeter. 
 
 i f 
 
 I I 
 
 VI. REVIEW. 
 
 MISCELLANEOUS DRILL EXERCISES 
 
 140. Make six dift'erent numbers with the figures 3, 9, and 8, 
 and find their sum. 
 
 141. Subtract 3 from every number between 10 and 30, and 
 then find the sum of the remainders. 
 
 142. Starting at Chicago I go 200 miles due west, then 150 
 miles due north, then 100 miles due east, then 350 miles due 
 souch, then 100 miles due east, then 160 miles due north. How 
 far from Chicago am I now ? What direction from the city am I ? 
 
 143. The remainder is 302105. If both subtrahend and minu- 
 end be multiplied by 101, what will the remainder be ? 
 
 144. Fm\i milk is worth 7 cents a quart. If 2 quarts of water 
 be mixed with every 3 gallons of milk, what will a quart of the 
 mixture be worth ( 
 
f»%\ 
 
 REVIEW. 
 
 loa 
 
 rs of water? 
 
 145. How n,any days between March 7 and N. /ember 23? 
 
 Finf^oJI^r"'" V^" remainder arul subtnihend i« 10011)0801. 
 riim ^UlOl times the minuend. 
 
 147. What nun.ber must be subtracted from i to leave .05? 
 
 148. What number subtracted 88 times from 80005 will leave 
 13 as a remainder ? *^® 
 
 ■^ 149. ;: 11 men can build a wall in 18 days, how manv men 
 wdl U take to build a wall three times as hmg in half Zume ? 
 
 160. How many nnnutes .re there between 35 minutes past 7 
 in tlio monung and midnight ? " pasw 
 
 161. What wui 3240 feet of lumber cost at |?22.50 per M ? 
 166. Find the prime factors of 01200. 
 
 « Im '^m 'I' ''■ f.- °' '■"" '"""''"•' '» '5' »•"' "'"'^ L- P- M. 
 
 IS 460. What are the numbers '( 
 
 y 
 
 muifth^^'T k'''/"''^ ^' P"'^ *^ ^ ^''^^^ •^^ ^^ f««t- How ion. 
 must the pile be to contain 8 cords / ^ 
 
 ei^m'fttu '^"''"''" T'''"'^ "^'^ '""'^^ ^^^"^ «f 22 sover- 
 »Wlh;gs ^'^'"*^^^^^^^"«' l'^ «^«-"«' 22 half-crowns, and 64 
 
 160. Reduce £5.375 to pound.,, shillings, and pence. 
 
 161. Reduce £12 I83. 6d. to dollars and cents. 
 
 162. Of a mixture of milk and water, f of the weight is water 
 How many ounces of water in a pound of the mixture ? 
 
-v^ 
 
 r 
 
 •^«" 
 
 K 
 
 104 
 
 FOURTH DEPARTMENT. 
 
 163. A pint of water is put into a gallon of milk. What part 
 of the mixture is water ? * 
 
 164. Subtract 23 from each prime number between 30 and 50, 
 and then find the continued product of the remainders. 
 
 166. At the rate of 124| rods a minute how many hours will 
 a train be in going from Boston to Buflfalo, a distance of 498 
 miles ? 
 
 166. How many miles an hour does a person walk who takes 
 X 2 steps a second and 1800 steps in a mile ? 
 
 167. A train runs from New York to Philadelphia, 90 miles, 
 in 1 hour 40 minutes. What is ita rate per hour ? 
 
 168. A horse traveled 5i miles in 33 minutes. W^hat was his 
 average time per mile ? 
 
 169. A can mow | of a field in days ; B can mow (| of it in 
 4 days. How long will it take both to mow the field ? 
 
 A 
 
 X 
 
 170. If * of a piece of work be done in 28 days, how much 
 will be done in 41 days. 
 
 171. What length of road 49i feet wide will contain an acre ? 
 
 172. How many sods, each 2 feet 6 inches by 10 inches, will 
 je required to sod an acre of ground ? 
 
 173. Find the cost of half an acre » J ground at 63 cents per 
 square yard. 
 
 174. How many days will 19,734 pounds of hay last 17 horses, 
 if each horse eats 33 pounds a day ? 
 
 175. Simplify 2i X a X 6J X I X § of ^ X 3^. 
 
 176. How many lots of | "acre each can be made out of a piece 
 of village of prop'^rty 45 chains square ? 
 
 177. Find the cost of 2064 pounds of wheat at 75 cents per 
 bushel. 
 
 178. From I of a score take the difference between ^ of a 
 hundred and '^ of a dozen. 
 
REVIEW. 
 
 105 
 
 179. A piece of cloth, when measured with a yard measure 
 that 18 I of an inch short, appears to be 141 yards long. What 
 is its true length ? 
 
 180. Find a man's wages f(,r 4 weeks 3 days 6 hours at $12 a 
 week, reckoning 6 days to a week and 10 hours to a day. 
 
 181. Divide 1^2652 into three parts, in the ratio of 6, 4, and 3. 
 
 182. A and B together have «^136, and g' of A's money is e,mal 
 to f of B's. How mucli has each ? 
 
 183. How many rods of fence will be required to enclose a 
 held m the shape of a rectangle, one side of whicl) is 64 rods 
 and containing 20 acres ? ' 
 
 184. Find tlie cost of 3920 bricks at $8.40 per M. 
 
 186. How many ties will it take for 20 miles of railway track 
 each yard requiring 1 tie ? ' 
 
 186. How many square yards in the ceiling, walls, and floor 
 of a ro<.m 28 feet long, 24 feet wide, and 18 feet high ? 
 
 187. Find the cost of a scantling 4 inches by 8i inches, and 22 
 feet long, at $18 per M. 
 
 188. What will it cost to floor a room 16 feet hm^ and 12 feet 
 wide at $14.50 per square of 100 square feet ? 
 
 189. What will it cost to paint the walls and ceiling of a hall 
 *Ld r ^*'"^' ^^ ^*'''* ""'^^^ ''''^ ^^ ^^^^ ^''^^' '*"* ^^-^^ P'''' '^"^'■*' 
 
 190. What will it cost to slate a roof 44 feet by 35 feet at 
 $5.75 per square of 100 square feet ? 
 
 191. What will it cost to paint the floor of a room 20 feet by 
 24 feet at 22 cents per square yard ? 
 
 192. What will it cost to plaster a room 16 feet by 20 feet 
 and 15 feet high, at 18 cents per square yard, allowing .Jj, for 
 doors and windows ? 
 
 ing 
 
 193. How many square feet in a walk 4 feet wide, surround- 
 a rectangular garden 50 feet bv 42 feet ? 
 
 y 
 
106 
 
 FOURTH DEPARTMENT. 
 
 194. How many feet of lumber in a close board fence feet 
 high, i inch thick, and 2 miles long ? 
 
 195. If a field 50 rods long contains 10 acres, how wide is the 
 field ? 
 
 196. If a field 200 yards wide contains 15 acres, how long is it '( 
 
 197. How many planks 10 inches wide and 13^ feet long will 
 it take to make a sidewalk 000 feet long and 4i feet wide ? 
 
 198. If each man occupies a space of 27 inches by 20 inches, 
 how many men can stand in a room 30 feet by 40 feet ? 
 
 199. How many trees are there in a wood a half a mile square, 
 if there are on an average 8 trees to a square chain l 
 
 200. A reservoir is 40 feet inches long and 21 feet 4 inches 
 wide. How many cubic feet of water must be drawn off to lower 
 the surfac<' 5 inches i 
 
 201. How many posts i)laced 8 feet apart will it take to go 
 around a quarter-section of land '! 
 
 202. How many cords of wood can be piled in a shed 72 feet 
 long, 48 feet wide, and 16 feet high ? 
 
 203. At 20 cents a cubic yard what will it cost to dig a cellar 
 36 feet long, 28 feet wide, and 7 feet deep '( 
 
 204. Fintl the length in inches of the edge of the largest square 
 marble slab that can be used in flooring a room 33 feet 10 inches 
 long and 24 feet 6 inches wide. 
 
 205. From a lot 80 rods scpiare I sold 80 square rods. What 
 is the value of the remainder at $160 an acre ? 
 
 208. The area of a certain floor is 1024 stjuare feet. The 
 length is 4 times the breadth. What are its dimensions ? 
 
 207. How many sods, each 8 inches s(iuare, will be required 
 to sod a yard 24 feet long and 10 feet 8 inches wide ] 
 
 208. A's farm is | mile square, B's contains | of a square mile, 
 and C's is | larger than A's and B's together. How many acres 
 in C's farm ? 
 
 I 
 
REVIEW. 
 
 107 
 
 -^ 
 
 209. At 36 cents a square yard how much will it cost to 
 plaster the walls and ceiling of a room 18 feet long, 16 feet wide, 
 and 9^ feet high, allowing 73 square feet for windows and door ? 
 
 210. The inside dimensions of a rectangular fort are 210 feet 
 and 180 feet. The stone wall surrounding this space is 5 feet 
 thick and 12 feet high. How many cubic feet of masonry are 
 there in the wall ? 
 
 211. Find the value of the lumber at $18 per M. that will be 
 required to build 500 yards of plank sidewalk 10 feet wide, 2 
 inches thick, and resting on 3 continuous lines of scantling 4 
 inches square. 
 
 212. Find the cost of a pile of lumber 16 feet long, 3 feet 3 
 inches wide, and 5 feet 6 inches high, at $22.50 per M. 
 
 213. A contractor undertakes to dig a ditch 3^ miles long, 12 
 feet wide at the top, 6 feet wide at the bottom, and 5 feet deep, 
 for 25 ce"ts per cubic yard. How much money should he receive 
 for the work ? 
 
 214. The length of a rectangular field whose area is 3g acres 
 is to its width as 16 is to 9. Find the cost c»f fencing it at $1.50 
 per rod. 
 
 215. A man has a square field containing 10 acres. How 
 many furrows must he plough across it to make an acre, suppos- 
 ing each furrow to be 8 inches wide ? 
 
 216. A map is drawn on a scale of 10 miles to an inch, and a 
 township is represented on it by a square whose side is half an 
 inch. How many acres in the township '\ 
 
 217. How long must a lot be to contain \ of an acre, if it is 88 
 fctt wide \ 
 
 218. Trees are planted 12 feet apart around the sides of a 
 rectjingular field 40 rods long, c.jntaining 2 acres. Find the 
 number of trees. 
 
 219. V square yard is cut from a board 18 feet long and 10 
 , iiiM vHc icnum ui Liiu lomamdei' f 
 
w 
 
 108 
 
 FOURTH DEPARTMENT. 
 
 220. A garden, 180 feet long by 150 feet wide, is surrounded 
 by a tight board fence (> feet high. What will it cost to paint 
 the fence, both sides, at 12 cents per square yard ? 
 
 221. How many square miles of country will be represented 
 by a map 10| inches long and inches wide, drawn on a scale of 
 3 miles (in length) to an inch ? 
 
 222. A boy takes 924 steps of 2^ feet each to walk round a 
 field 40 rods long. How many acres in the field ? 
 
 223. A farmer has a bin 18 feet long, 10 feet wide, 6 feet deep, 
 that is I full of wheat. What is the wheat worth at $2 a bushel ? 
 
 NoTR.— A bushel contains 2150i cubic inches. 
 
 224. I want to cut an acre of land from a long, narrow field, 
 which is 55 yards broad. What length of it must I take ? 
 
 225. There are 107 square yards in the surface of the walls 
 and ceiling of a room 15 feet by 18 feet. How high is the room? 
 
 226. A gallon of paint, worth $1. 75, covers 200 square feet. 
 What will it cost to paint a tight board fence 4 feet high, which 
 encloses a lot 8 rods by 12 rods? 
 
 227. What must be the width of a box G feet long, 4 feet 
 high, to contain | of a cord of wood ? 
 
 228. A map 6 feet loag and 4 feet broad represents 13,824 
 square miles of the earth's surface. To what scale is it drawn ? 
 
 220. How many bushels of wheat in a bin 391 inches long, 11 
 feet wide, and filled 4| feet deep? 
 
 230. A grocer received pay at 72 cents a pound for what he 
 supposed to be 5^ pounds of tea. His pound weight was one- 
 half ounce too heavy. How much money should he have 
 received ? 
 
 231. How many bushels of barley will weigh as much as 690 
 bushels of com ? 
 
 232. How many square yards of block pavement in a street 
 ^ a mile long and 1| chains wide ? 
 
REVIEW. 
 
 109 
 
 1 ? ?: T"" '**^'^ ^'^ '"''"^y *™"'^« ^i» five sons. He Kave 
 i to the eldest,, J of what v-as left to the second, f of what was 
 then left to the third, ? of what was then left to the fourth and 
 the remamder, which was $280, to the fifth. How much money 
 was divided ? -^ 
 
 flfth7^«o?"S«'ir"''T""*?' *''"''"' '^*'°"« together to find the 
 
 234. A merchant mixes 22 pounds of coffee worth 45 cents 
 worth ? ' '''''^^ ^^ """*''• ^^^'^* '" ^ ^""""^ ^^ *'^^ '"^^^^^^ 
 
 235. If 24 men can do a work in 14 days of hours how 
 many men will do it in 12 days of 7 hours i 
 
 n.,?«f ; ^- "^Vr ^? ^''^' *" ^'^ ^' ^"^ "^^"y yards' start 
 must A give B to make an even race ? 
 
 237. A garrison of 2000 men has provisions for 60 days At 
 the end of 20 days a reinforcement arrives, and then the pro- 
 visions last only 5 days. What is the number of the reinforce- 
 
 238. If a man rows 10 miles in 2^ hours against a stream, the 
 rate of which is 3 miles an hour, how long will he be rowing .5 
 miles with the stream ? ^ 
 
 239. If the shadow of an upright pole 9 feet high is Sf feet 
 what wil be the height of a church spire which casts a shado; 
 J21 feet long ? 
 
 240. Show that the highest common factor of two numbers is 
 the least common multiple of all their common measures. 
 
 ^1. A can do f of a piece of work in 8 hours, and B can do 
 i of the remainder in 2 hours, and C can finish it in 40 minutes 
 m what time will they do it, aU working together ? 
 
 242. By using false weights a grocer receives 33 cents instead 
 of 32 cents. Find the number of ounces in his false pound. 
 
 243. Find the number of feet, board measure, in 25 joists, each 
 b inches by 6 inches, and 18 feet long. 
 
 I 
 
110 
 
 FOURTH DEPARTMENT. 
 
 MISCELLANEOUS BUSINESS EXERCISES. 
 
 244. Cash. —On hand at the beginning of the day, $572.20. 
 Received during the day, $426.95. Paid, $65.80. What is the 
 cash balance at the end of the day? 
 
 246. Cash.— On hand at the beginning of the day, $273.87. 
 Received during the day, $243.10. On hand at the close of the 
 day, $362.42. How much was paid ? 
 
 246. Cash.— On hand at the beginning of the day, $5200.25. 
 Paid during the day, $353.98. On hand at the close of the day, 
 $6056.83. How much was received? 
 
 247. Cash.— Received during the day, $10.23. Paid during 
 the day, $16.63. On hand at the close of the day, $2.45. How 
 much was on hand at the beginning of the day? 
 
 248. Cash.— On hand January 1, $240. On deposit in the 
 Merchants' Bank, $524.80. Received during January, $485.50. 
 Paid during January, $562.80. Deposited cash, $66. Find the 
 amount of cash on hand and the amount on deposit January 31. 
 
 Direction.— t ill the blanks below with the answers to Exercise 248. 
 
 249. Cash.— On hand February 1, . On deposit in the 
 
 Merchants' Bank . Received during January, $329.84. 
 
 Paid during January, $134.15. Deposited, $124. Find the 
 amount of cash on hand and the amount on deposit February 28. 
 
 250. Cash.— On hand March 1, . On deposit in the 
 
 Merchants' Bank, . Received during March, $463.42. Paid 
 
 during March, $69.34. Deposited, $510.45. Find the amount 
 of cash on hand and the amount on deposit March 31. 
 
 251. Merchainiise,— On hand at the beginning of the year, 
 $1428. Bought during the year, $2143. Sold during the year,' 
 $3627. None on hand. Find the gain or loss. 
 
 252. Merchandise.— None on hand at the beginning of the 
 year. Bought during the jear, $4215.74. Sold during the year, 
 $1565.85. On hand at the close of the year, $2742.79. Find 
 the gain or loss. 
 
 I 
 
REVIEW. 
 
 Ill 
 
 JA^'J^n'^ff^-r^'' ^"^^ "^ *'^^ ^«8i"'"»« of the year. 
 £ ; . ^"^^* ^"""^ ^''^ y^*^' ^3142. 80. Sold during the 
 year, $5117.35. None on hand. Find the gain or loss. 
 
 Ssf^t'.^^'"*'^^"'^!^®-"^" ^'""^ "* ^^^ ^^g^""^"g «f th« year, 
 ' t;. o'. ""^ ^^"^^^ ^"""S the year. Sold during the 
 year $17,342.96. On hand at the close of the year, $16,399 13 
 Jf md the gam or loss. 
 
 265. Merchandise.-None on hand at the begiiming of the 
 
 IZ $98Srl* n""? *^' ^'"'' ^1^'242.87. Sold during the 
 year $9836.44. On hand at the close of the year, $5241.54. 
 J^ nid the gam or loss. 
 
 $7m Vf ^ R ^''?.'^^^^:~^" ^'"^ "' '^' ^^^^"'^'"g «f the year, 
 fo; ^"^^^ "^"""^ *^'^ y^^^' $3624.87. Sold during the 
 year $8319.54. On hand at the close of the year, $2143 82 
 i^ md the gam or loss. 
 
 $if/2o^5^'t^''^!'!'~''' ^r' '* ''"' '^^"^""^^ "^ ^^- y-^' 
 
 $16,120.25 Bought durmg the year, $5321.70. Sold during 
 the year, $13,617.18. On hand at the close of the year, $125 18 
 Fmd the gain or loss. . ff - -xo. 
 
 268. Hardware.-On hand January ], $15,024. None 
 bought durmg the year. Sold during the year, $7,342 94 On 
 Jiand at. tlie close of the year, $6524. Find the gain or loss. 
 
 259. Boots and Shoes.-On hand January 1, boots and 
 shoes valued at $5921.47, and stock valued at $2320. Bought 
 durmg the year, boots and shoes at a cost of $3462 Manufac- 
 tured the stock into boots and shoes at an expense of $1462 
 
 firV^'l ^T' ^^^^*- ^"^'^ ^''' ''' f"^"^^« goods valued 
 at $145. On hand at the close of the year, boots and shoes 
 valuea at $4964. Find the gain or loss. 
 
 260. Real Bstate.-Owned at the beginning of the year 
 property valued at $15,620. Bought during the year property 
 
 r^o *i;S ^"^ ^''^^''- ^"^*^ ^"'^"^ *^" y«*^ property amounting 
 to $12,400. Value of property on hand at the close of the year 
 $9020. Find the gain or loss. ^ ' 
 
 I 
 
112 
 
 FOURTH DEPARTMENT. 
 
 
 ■ 
 
 i 1 
 
 ' 1 
 
 f 
 
 1 
 
 "■;i 
 
 261. Real Estate.- Owned on January 1, 1884, property 
 valued at $6621. Bought during the year, $9846. Property^ 
 destroyed by fire during the year, $1276. Sold during the year, 
 $7263. On hand December 31, $5364. Find the gain or loss. 
 
 262. Real Estate.— Owned at the beginning of the year, 
 $16,324. Bought during the year, $11,372. Property destroyed 
 by fire during the year, $3621. Sold during the year, $20,115. 
 On hand at the close of the year, $6389. Received insurance on 
 property destroyed, $1225. Find the gain or loss. 
 
 263. Dry Goc ds.— On hand at the beginning of the year, 
 $12,248.50. Received free, from a friend, goods valued at $4200. 
 Sold during the year, $16,240. On hand at the close of the 
 year, $1,142.85. Find the gain or loss. 
 
 264. Groceries.— On hand at the beginning of the year 
 groceries valued at $9324.80. Bought during the year, $2421.75. 
 (iroceries destroyed by fire during the year, $1314. Sold dur- 
 ing the year, $8465.26. On hand at the close of the year, 
 $3662.80. Find the gain or loss. 
 
 265. Provisions.— None on hand at the beginning of the 
 year. Bought during the year, $7321.75. Provisions destroyed 
 by fire, $984.20. Sold during the year, $4241.80. Received 
 insurance, $600. On hand at the close of the year, $2116.90. 
 Find the gain or loss. 
 
 266. Lumber.— On hand at the beginning of the year, 
 lumber and logs valued at $4620. Bought during the year, logs 
 at a cost of $3610. Manufactured lumber valued at $7966, at 
 an expense for labor of $810. Sold lumber during the year, 
 $8650. Lumber and logs on hand December 31 are valued at 
 $6625. Find the gain or loss. 
 
 267. Furniture. —On hand at the beginning of the year, 
 $4936.56. Bought during the year, $7428.40. Sold during the 
 year, $8420.90. Furniture destroyed by fire during the year, 
 $1049. On hand at the close of the year, furniture valued at 
 $5620. Received insurance on furniture destroyed, $850. Paid 
 insurance expenses, $25. Find the gain or loss. 
 
 -»-.•, .=iS= li 
 
FIFTH DEPAKTMENT. 
 
 I. PERCENTAGE. 
 
 HINTS AND DEFINITIONS. 
 
 The baHe is the „„„,ber on which the percentage is co.nputed. 
 baselTbr^aVer '" ''' """"''^' ^''''"^ '^«-*- »•- -any hundredths of the 
 
 Fractional Equivalents. 
 
 50% zr.S-) =J. 
 
 33i% = .33i = i. 
 26% =.25 =J. 
 20% =.20 =J. 
 
 16|% = .ieij = i. 
 12J% = .l2i = J. 
 10% =.10 =,],. 
 84% = .08i = A. 
 
 6i%=.06J = A. 
 6% =.05 =^. 
 
 3i% = .03J = 3\,. 
 2i% = .02i=^. 
 
 EXERCISES FOR MENTAL DRILL. 
 N0TB.-D0 not use pen or pencil. 
 
 1. What is ^ of 396 ? 
 2.. What is ^ of 488 ? 
 
 3. What is + of 595 ? 
 
 4. What is ^ of 966 ? 
 6. What is ^ of 968 ? 
 
 6. What is I of 428 ? 
 
 7. What is f of 635 ? 
 
 8. What is f of 816 ? 
 
 9. What is T^ of 950 ? 
 10. Wliat is i\ of 732 ? 
 
 11. Find8J% of $672. 
 
 12. Find 25% of $480, 
 
 13. Find 20% of $560. 
 
 14. Find 10% of $327. 
 16. Find 75% of $244. 
 
 16. Find 60% of $720. 
 
 17. Find33J%of$792. 
 
 18. Findl6f% of $624. 
 
 19. Find 12^% of $848. 
 
 OA f.^j OH 1 ^ » — 
 
 «v, i iiiu u,- 2 /f or $yw. 
 
114 
 
 FIFTH DEPARTMENT. 
 
 WRITTEN DRILL BXBROISBS. V 
 
 21. What fraction of 88 is 11? V/hat per cent? 
 
 22. What fraction of $200 is $5 ? What per cent? 
 
 23. What is the diflference between 2^% and 3^% of $800? 
 
 24. A clerk who received $325 a ytar had his salary raised 
 40%. What does he receive now? 
 
 26. Some property which cost $3256 increased in value 125%. 
 What was the increased value? 
 
 26. A regiment went into battle with 1060 men, and came out. 
 with 588 men. What per cent was lost ? 
 
 27. The rent of a house is $330, which is 11 % of its value. 
 What is its value ? 
 
 28. A merchant sold $4800 worth of goods, and had 33J% of 
 his stock left. What was his entire stock worth ? 
 
 29. A lawyer collected $3264, and charged 5% for his ser- 
 vices. How much did he pay over ? 
 
 30. Ten years ago the population of a city was 32,480, It 
 has increased 20%. What is its present population? 
 
 31. An estate agent sells a house and lot for $8565, and re- 
 ceives 6% for his services. How much money does he receive? 
 
 32. A horse that cost $220 was acid for $242. What was the 
 gain per cent. 
 
 33. A farm was sold for $7490, which was 16^% more than it 
 cost. What did it cost? 
 
 34. What number increased by J of 25% of itself equals 867? 
 
 Z5r. Ten years ago the population of a city was 26,275. Its 
 present population is 31,530. Find the increase per cent. 
 
 36. If gunpowder contains 75% of saltpetre, 10% of sulphur, 
 and 15% of charcoal, how many pounds of each are there in a 
 ton of powder ? 
 
 I 
 
came out 
 
 ________^^ PERCENTAOE. ^j- 
 
 F uiorit. What did he pay per barrel? 
 
 F m .or inem. What did he pay per head ? 
 
 40. If goods are bought for $8728 and sold for aosiO ^.h., 
 18 the gam per cent? V-'oii^, what 
 
 What W.11 oe gamed per cent by selling the fa™, for »oOOO! 
 
 caT' nrr''*t "Ti';'" ""'=''' *^-^' >>"' take, off 6% for 
 ««.h. If h.8 profit ,,33%, what wa, the cost of the articled 
 
 47. What would a dishonest dealer sain oei- ™„. i.., • 
 weight of 16 ounces instead of a poundf ^ ""« * 
 
 48. What per cent above cost must a man mark hi<, <,„„j • 
 
 :i: ^;' o^: t^c^:." -^ ^'^ -- - ^^^^tr^r rr^i- 
 
 ou^;sVwat:^'ttr "T.' 0° '*""' "' "■"' ■"»-'-'> * 
 
 its preselr^S-tt tlT''"' " ''""""^'- ^"-^ >«' -' »' 
 
IIG 
 
 FIFTH DEPARTMENT. 
 
 51. By Belling a farm for J2340 an estate dealer lost 10 y!^ 
 of the cost. What ought he to have sold it for to make 10% i 
 
 62. If resin is melted with 33^ % of its weight of tallow, what 
 per cent of tallow does the mixture contain? 
 
 63. How many gallons of water nnist be mixed with 29^ gal- 
 lons of wine in order that the mixture may contain 17 J % of 
 water? 
 
 64. A merchant increases his capital annually by 20% of itself. 
 At the end of four yeurs his capital is $95,040. What was his 
 capital at first ? 
 
 66. The sum of 10 % of a number and 5 % of half the remainder 
 is what per cent of a quarter of the number ? 
 
 66. A quantity of sugar was sold at 10% gain. If it had cost 
 $120 more the sam ; selling price would have entailed a loss of 
 10%. Find the cost of the sugar. 
 
 ^ IH 
 
 f i 
 
 II. TKADB DISCOUNT. 
 
 HINTS AND DEFINITIONS. 
 
 When a reduction is made from tlie noviinal price of an article, from the amount 
 of a debt, or from the face of a note, it is called a discount. 
 
 Some kinds of merchandise-books, furniture, musical instruments, etc.— have 
 fixed prices. Manufacturers and wholesale dealera invoice such merchandise to the 
 trade, or retail dealers, at the fixed or list prices. 
 
 The list prices are usually the retailer's Selling prices. 
 
 The manufacturer or wholesale dealer allows the retailer a trade discount 
 whit!, i 1... ' u.'fai ; at a certain rate per cent from the face of the invoice. ' 
 
 The amon.iH •>( the discou. ♦ a.lowed depends sometimes upon the amountof the 
 OK joHivimes u^yon the terms of settlement. 
 
 Very often two or mpre discounts are deducted in succession. Thus 10% and 
 6% off, or as it is generally expressed in business, 10 an' r> off, means a discount of 
 10%, and then 5% from what is left; 20, 10, and 5 c ueans three successive 
 discounts. 
 
 A retailer's profit is smaller wh^n he is allowed 10% and 6 oif than if he were 
 allowed 15/C off. 
 
 The result is not affected by the order in which the discounts are taken. 
 
 I 
 
TRADE DISCOUNT. 
 
 117 
 
 ['emainder 
 
 the amount 
 
 lountof the 
 
 ILLUSTRATIVE EXBROISBS. 
 coi ?^*''^" ^"^ '"'''^^'^^d at $80, less 20 % and 10 % . What do they 
 
 980.00 
 
 J16^ Multiply by 2 and carry one place to the right 
 
 $64.00 
 
 ^•^Q Multiply by 1 and carry one place to the right 
 $57.80 Am. 
 
 2. Good, are invoiced al »243.27, with 40, 20, and 5 off. Find 
 tne cost. 
 
 $243.27 
 
 ^97^8 Multiply by 4 and carry one place to the right 
 
 $145.96 
 
 ^29J9 2 Multiply by 2 and carry one place to the right. 
 
 $116.77 
 
 ^^ •"^ ® '^*''e half and carry two places to the right, 
 $110.93 Am. 
 
 ca,eMnhede.i:anf.^o1C:Sdirt;t^^^^^^^^^^^ 
 
 Find?hetos:" ''^'^'"' '' '''''''^ ^^^^ ^^*' ^^' -<^ ' ^^^ 
 
 $324.45 
 108.15 Take one-third. 
 
 $216.30 
 
 ^•^ ^ ^^''^ one-fovfth and carry two places to the right 
 
 $210.89 
 
 ^^ Multiply by 1 and carry two places to the right 
 
 $208=78 Ans. 
 
5C <gfc.- 
 
 I ll 
 
 I il 
 
 118 
 
 FIITH DEPARTMENT. 
 
 4. Goods are invoiced at $236.18, with 40, 6, and i off. Find 
 the cost. 
 
 $236.18 
 
 ^^•^ 7 Multiply by 4 and carry one place to the right. 
 
 $141.71 
 
 8. 50 Multiply by 6 and carr- two places to the right. 
 
 $133.21 
 
 .67 Multiply by J and carry two places to the right. 
 
 $132.54 Ans. 
 
 BUSINESS EXERCISES. 
 Direction.— Find the cost price. 
 
 67. List price, $243. Trade discount, 5 and 20 off. 
 
 68. List price, $380. Trade discount, 5 and 30 off. 
 
 69. List price, $340. Trade discount, 30 and 5 off 
 
 60. List price, $649. Trade discount, 50 and 5 off. 
 
 61. List price, $954. Trade discount, 60 and 5 off. 
 
 62. List price, $472. Trade discount, 20 and 3 off. 
 
 63. List price, $380. Trade discount, 10 and 8 off. 
 
 64. List price, $684. Trade discount, 20 and 1 off. 
 
 65. List price, $998. Trade discount, 10 and 4 off. 
 
 66. List price, $651. Tra^e discount, 30 and | off. 
 . 67. List price, $690. Trade discount, 40 and | off. 
 
 68. List price, $200. Trade discount, 20 and 10 off. 
 
 69. List price, $485. Trade discount, 10 and 20 off. 
 
 70. List price, $320. Trade discount, 40 and 20 off. 
 
 71. List price, $252. Trade discount, 10 and 10 off. 
 
 72. List price, $843. Trade discount, 30 and 40 off. 
 
 ii' i 
 
TRADE DISCOUNT. 
 
 119 
 
 73. List price, 1^500. Trade discount, 2^ and J off. 
 
 74. List price, f 384. Trade discount, 10 and 2^ off 
 76. List price, 0333. Trade discount, 50 and 12* off 
 
 76. List price, ^80. Trade discount, 33^ and 5 off 
 
 77. Invoiced price, $1020.45. Discount, 10, 5, and 3 off 
 
 78. Invoiced price, $2142.45. Discount, 5, 2*, and J off 
 
 79. Invoiced price, |402.18. Discount, 20, 5, and 2| off 
 
 80. Invoiced price, $104.80. Discount, 10, 8 J, and ^ off 
 
 81. Invoiced price, $692.45. Discount, 40, 10, and 5 off 
 
 82. Invoiced price, $804.20. Discount, 50, 30, and 1 off 
 
 83. Invoiced price, $201.13. Discount, 30, 20, and 10 off 
 
 84. Invoiced price, $404.50. Discount, 20, 10, and 3^ off 
 86. Invoiced price, $930.00. Discount, 33^ 20, and 2| off 
 
 86. Invoiced price, $224.40. Discount, 25, 16|, and 12| off 
 
 87. Tlie gross an.ount of a bill of merchandise is $186 36- 
 lid '20%*^'*" ""'* ''"'''""'" ^^' '^^^' ""^ '^^''''"^* ^^"^g 30% 
 
 88. What direct discount is equivalent to a discount of 20% 
 and 10% ? 
 
 on??' ^I'f ,^'^^^*^ discount is equivalent to a discount of 33i%, 
 
 dv % , and 1 % ? "^ ' 
 
 f ^'^^^f '' *^^ difference on a bill of $425 between a discount 
 ot D0% and a discount of 30% and 20%? 
 
 91. A book broker buys books at 20% and 10% from the cata- 
 logue prices, and sells them at an advance of 10% on catalogue 
 prices. What per cent profit does he make ? 
 
 «.-?n' "^Vf ''* ^"^' ^ P'^"^'' *^^ "«* P"««« «f ^hich are $420, 
 $b30, and $800. He is allowed 20 and 10 off He sells the 
 pianos at an advance of 50% on the cost prices. ind his total 
 profit. 
 

 120 
 
 FIFTH DEPARTMENT. 
 
 f 
 
 93. A retail bookseller buys at a discount of 20, 10, and 5 off 
 and sells at list prices. What per cent profit does he make ? 
 
 94. A merchant buys furniture at 20% and 10% from list 
 prices, and sells it at 10% and 5% from list prices. What per 
 cent profit does he make ? 
 
 .^o?.*/ "^"^'"^ machine agent buys r>0 machines at a discount 
 of 30% and 16f %. He sells them at an advance of 5% on the 
 list price. Find his profit on each. 
 
 III. INVOICES. 
 
 HINTS AND DEFINITIONS. 
 An invoice is a detailed statement of merchandise sold by one dealer to another 
 The place and date of sale, and the names of the buyer and seller, should be given 
 
 invoilTl**?' *'r' ''*"^'^*^"' '""^ abbreviations made use of in making out 
 invoices, are given below: — * 
 
 Al First quality. 
 
 «-'/ Care of. 
 
 Do Ditto, the same. 
 
 Com Commission. 
 
 Bxs Boxes. 
 
 Bgs Bags. 
 
 Bbl Barrel. 
 
 Bal Balance. 
 
 Fol Folio or page. 
 
 I"8t Present month. 
 
 Prox Next month. 
 
 Ult Last Month. 
 
 Mdse Merchandise. 
 
 Memo Memorandum. 
 
 No. or J Number. 
 
 Per By, or by the. 
 
 Shipt Shipment. 
 
 C- O. D Collect on delivery. 
 
 BUSINESS EXERCISES. 
 
 96. Books.-New York, January 3, 1886. S. R. Warner & 
 Co., Toronto, Ont., bought of A. S. Barnes & Co., 12 sets New 
 National Readers at $1.76; 3 Popular History of the United 
 States at $5 ; 5 Monteith's Science Reader at $1 25 • 18 Sill's 
 Lessons in English at 90c. ; 14 Comprehensive Geography at 75c • 
 24 Practical Arithmetic at 80c. ; 18 Steele's Chemistry at $1 20 • 
 12 Steele's Physiology at $1.20; 18 Watson's Elocution at 40c' 
 Less 30% and 10%; 36 doz. Copy Books at 65c. per doz. net"; 
 40 doz. Drawing Books at 75c. per doz. net. Packing 75c. 
 
INVOICES. 
 
 121 
 
 NoTB—InvolcM are very different in detail. No rules for the guidance of rtu- 
 dent* can be given. The peculiar methods of any particular business house 6«u 
 T>e learned only by actual practice in that house. Tho exercises which follow are 
 intended for general business practice. 
 
 [Exercise 96.] 
 
 New York, Jan. 3, 1886. 
 
 ■ 
 
 s. 
 
 R. 
 
 Warner &> Co., 
 
 
 
 
 
 
 1 
 
 joronto, Ont., 
 
 1 
 
 ^ougbt oi A. S. Barnes &> Co. 
 
 Terms cash. 
 
 ^H 
 
 
 12 
 3 
 5 
 18 
 14 
 24 
 
 Sets New National Readers 
 Popular History of U. S. . 
 Monteith's Science Primer 
 Sill's Lessons in English . 
 Comprehensive Geography 
 Practical Arithmetic , . 
 
 . $1.75 
 
 . 500 
 
 . 1.25 
 
 .90 
 
 .75 
 
 .80 
 
 21 
 
 ** 
 
 * 
 «« 
 ** 
 
 00 
 
 •« 
 «* 
 *• 
 «* 
 «» 
 
 1 
 
 
 1 
 
 
 18 
 12 
 
 18 
 
 Steele's Chemistry .... 
 Steele's Physiology .... 
 Watson's Elocution .... 
 
 1.20 
 
 1.20 
 
 .40 
 
 «* 
 #* 
 
 * 
 
 «* 
 ** 
 
 . 
 
 
 I 
 
 
 
 
 «*4r 
 
 #« 
 
 
 
 1 
 
 
 
 Less 30% and 10% 
 
 «* 
 
 «♦ 
 
 *« 
 
 «* 
 
 
 
 36 
 40 
 
 Doz. Copy Books. Net . . .65 
 Doz. Drawing Books. Net . .75 
 
 Packing .... 
 Certified correct. 
 
 
 
 ** 
 
 *# 
 75 
 
 1 
 
 
 1 
 
 A. S. Barnes & C 
 
 0. 
 
 
 
 
 
 NoTB.-When goods are shipped from one country to another the sender of the 
 goods sends a certifled invoice-an ordinary invoice with the words "certified 
 correc and the signature of the seller. Such an invoice is accepted as correct by 
 the collectors of customs. ' 
 
122 
 
 FIFTH DEPARTMENT. 
 
 H 
 
 97. Dry Goods. -ChicaKo, January 5, 1886. Messrs. E. T. 
 Stone & Co., Grand Rapids, Mich., bought of William Cross & 
 ^on, 24 pieces Gordon Prints, 48 yds. each, at 6ic. ; 18 piece* 
 
 PrLT:5 T'\'' '''- '^'''' ""' ^^-^ '' P-- Standard' 
 Prints, 45 yds^ each, at 4c.; 20 pieces American Prints, 50 yds. 
 each, at 6c. Cooperage $1.25. 
 
 S W 5;*^'^ft^°od«--Wilmington, Del., Januaiy 9, 1886. 
 S. W. Clark & Bro, Kansas City, Mo., bought of James Morrow 
 
 «s!r'A '; ,u ;^"*'^'' ^' *^-^^' ^ d^^- « 1^- Peaches at 
 l^t' V\l?,^«™"*"e«at$1.90; 3 doz. 2| lb. Apricots at- 
 «!J.90. Less 5% for cash. Cooperage {K)c. 
 
 P^- 5°°^f --Philadelphia, Pa., February 3, 1886. Canada 
 Publishing Ca, Toronto, Ont., bought of J. B. Lippincott Co., 
 15 Dickens Peoples Edition, 15 vols., at $22.50; 7 George 
 
 f *'i; ? "nl" r' f ^' ^^ Thackeray, Globe Edition, 12 vols , 
 at $15 ; U Charles Reade, 17 vols. , at $21. 25 ; 36 The ' ' Duchess " 
 Novels at $1. Less 40%, 10%, and i%. Cooperage $1.20 (A 
 certified invoice necessary). 
 
 R^5;,^'"?r®e~^^^^™°'"' ^^^ ^^^^^ 12, 1886. James. 
 R Wallace & Co., Syracuse, N.Y., bought of H. Chisholm & Co., 
 3 bbls. Granulated Sugar at $7.50 ; 17 boxes Raisins at $1.75 • 4 
 boxes Layer Raisins at $2.15; 15 lbs Spice at 16c.; 24 boies 
 Currants at $1.40 ; 2 bags Rio Coffee at $27.20; 2 bbls. Syrup at^ 
 
 CartagI $1 5o'" ''^' ^^ ^^'' ^^'"^^ '^'''''""^' ^^ ^"^ ^ ^^• 
 
 lOL Fruit. -Rochester, N. Y., August 13, 1880. S. R. Rilev 
 
 M.1 ,,. '''^'"^' "^^ ^''"^'^^ °^ ^- P- Wallace & Son, 273 
 
 q«^K r*S'/P^^'' ^' ^^•^^' 1^^ ^^1«- ^^" Apples at $1.05; 
 362 busk Plums at $2. 12 J; 163 baskets Peaches at 63c.; 428. 
 baskets Pears at 42c. Less 20%. Cartage $12.86. 
 
 F^^'iflf'^u ^^^ Feed.-Montreal, Que., April 15, 1886. 
 rf ^K? ^f ' S^erbrooke, Que., bought of Thompson, Watt & Co., 
 13 bbls. Best Flour at $5.30; 14 bbls. No. 2 Flour at $4.75; 32 
 bbls. Pork at $18.90; 942 lbs. Hams at 13c.; 432 bush. Oatl at 
 ^Ic. ; 15 cwt. Bran at 55c. Less 33^%, 10%, and 2%. 
 
COMMISSION. 
 
 123 
 
 103. Hardware.-Toronto, Ont., March 13, 1886. Hugh 
 Cleland, Meaford, Ont., bought of Rice Lewis & Son, 200 Car- 
 riage Bolts at $2.25 per C. ; 150 Carriage Bolts at $3.15 ; 5 doz. 
 R. S. K. Knives at $2.14 ; 4^ doz. Pieced Bread Faoa at $2; 15 
 Eureka Stoves atfl4.90 ; 13 Royal Coal Stoves at $18.40 ; 6 Iron 
 Posts at $1.30. Less 7 % for cash. 
 
 104. Furniture.— San Francisco, Cal., May 3, 1886. G. W. 
 Powell & Bro., Denver, Col., bought of Thompson & King, 22 
 Bedroom Sets at $32.50; 18 Parlor Sets at $42.75; 6 Walnut 
 Sideboards at $18.25; 12 Walnut Dining Tables at $21.30; 14 
 Cherry Book Cases at §13.50; 17 Easy Chairs at $4.35. Less 
 40%, m%, and 2|%. 
 
 105. Lumber.— Detroit, Mich., November 18, 1886. The 
 Western Lumber Co., Milwaukee, Wis., bought of Patterson 
 Bros. & Co., 293,500 ft. Pir , first quality, at $42; 132,600 ft. 
 Pine, third quality, at $16; 425,250 ft. Hemlock at $22; 83,750 
 ft. Basswood at $26; 48,650 ft. Elm at $72.50. Less a regular 
 discount of 37i%, and 5% additional for cash. 
 
 IV. COMMISSION. 
 
 HINTS AND DEFINITIONS. 
 
 Commission is an allowance or compensation to an agent, commission mer- 
 chant, or factor. 
 
 Commission merchants are usually placed in possession of the goods bought or 
 sold. 
 
 The business of a broker is similar to that of a commission merchant. Brokers 
 do not have possession of the merchandise bought or sold. 
 
 The term broker is more generally applied to these whose business it is to buy 
 and sell stocks, bonds, notes, etc. 
 
 The person for whom the business is transacted is called the principal. 
 
 The person who sends goods to be sold is called the consignor or shipper. 
 
 The name consignment is given to the goods sent. 
 
 The person to whom the goods are sent is called the consignee. 
 
 The net proceeds of a consignment io the balance due the consignor after 
 charges and expenses have been deducted. 
 
 The commission or brokerage for buying or selling merchandise or real estate is 
 usually estimated at a certain per cent of the amount invested or realized. 
 
124 
 
 FIFTH DEPARTMENT. 
 
 BUSINESS EXERCISES. 
 
 106. An estate dealer sells a house and lot for $5620 at 2A%. 
 What is his commission for selling ? 
 
 107. A salesman receives 2^% of his sales. His sales for a 
 certain week amounted to $943.50. What was his commission 
 for that week ? 
 
 108. What must be a traveler's sale'^ for one year that he 
 may, at 3% commission, have a yearly income of $2400? 
 
 109. A lawyer collected a note of $242.50; how much should 
 he pay to the owner of the note, his commission being 8% ? 
 
 110. My attorney collected 80% of a debt of $5500, and 
 charged 7^% commission. What amount should he pay me ? 
 
 111. My agent sold my house and lot for $4850. He bought 
 me a new house and lot for $3725. His commission for selling 
 was 4 % , and for buying 2 % . How nmch cash should I receive ? 
 
 112. What is the amount of the sales when the brokei-age 
 charged is $64 at i%? 
 
 113. What is the amount of the sales when the net proceeds 
 are $2493.16, brokerage |%? 
 
 114. Sent $414 to an agent to be invested in prints at 13 
 cents a yard, after deducting his commission of 2i% of the sum 
 sent. How many yards can he purchase ? 
 
 •n^T!""^^''^ '''"""■**^ **'^ commission should be reckoned on tlie actual sum 
 
 115. My agent in St. Paul buys for me 3245 bushels of wheat 
 at $1.08. What is his commission at i % ? 
 
 116. Sent $6180 to a commission merchant to invest in flour 
 his commission being 3 % on the amount expended. How many 
 barrels of flour, at $4. 80 per barrel, can he purchase ? 
 
 117. An estate agent sells 420 acres of land at $18.50 an acre 
 and charges 2^ % commission. What is his commission ? 
 
OOMMISSICN. 
 
 125 
 
 118. A commission merchant sells a consignment of wheat tor 
 «7240. He pays ^2 for freight and storage, and charges a com- 
 mission of 2i % . What are the net proceeds ? 
 
 119. An agent charges 5^ % commission, and receives $441 for 
 his services. Find the amount of his sales. 
 
 120. A merchant buys, through an agent, 480 yards of carpet 
 at 80 cents per yard, and pays the agent |% commission. The 
 freight amounted to $1.92. At what price per yard must the 
 carpet be sold to realize a profit of 33J%? 
 
 121. A book agent receives a commission of 25% on the gross 
 amount of his sales, $1 for each book sold, and a salary of |l20 
 a year. During a certain year he sold 480 books at $7 each 
 What was his income for that year ? 
 
 122. A country merchant receives a commission of 16f % for 
 selling mowing and reaping machines. He sells during a certain 
 season 3 of the former at $90 each, and 5 of the latter at $120 
 each. His expenses connected with the sales were $17.50. Find 
 his profit. 
 
 123. A young man established a newspaper subscription 
 
 Xr^'x. "• ' '''^''''''' '*"'"" ^^^-^^ ^ "'""*^' ^"d hi« commission 
 20/.. During 1885 he received 130 subscriptions at $G each 
 142 at $4, 360 at $2, 182 at $1.50, and 573 at $1. What was his 
 net income for the year ? 
 
 124. An agent received $1269 with which to purchase goods 
 after deducting his commission of 5|% of the sum actually in- 
 vested. Find his commission. 
 
 125. A manufacturer sent $5202 to a leather dealer with which 
 to purchase leather at 2% commission on the sum invested 
 How much commission should he deduct ? 
 
 126. A worked B's farm of 320 acres for one year " on shares " 
 A received 25% of the gross receipts for his labor, and the 
 balance was divided equally. Wheat was raised on the entire 
 farm ; it yielded 28 bushels to the acre, and was sold at $1 12A 
 per bushel. Find B's sharo nf fho p,..>fi+a ^ 
 
126 
 
 FIFTH DEPARTMENT. 
 
 V. TAX3S. 
 HINTS AND DEFINITIONS. 
 
 Taxes are sums of money assessed on persons, property, or incomes, to defray 
 t.ie expenses of a country or corporation. 
 
 Real estate is fixed property, as lands and houses. 
 
 Personal property is movable property, as money, goods, furniture, ships, 
 cattle, htocks, etc. 
 
 An assessor is an officer appointed to estimate the value of property. 
 
 A capitation or poll tax is a tax assessed, without regard to property, upon 
 the person of every adult male citizen not exempted by law. 
 
 A licentte is a written permit to conduct a certain business, and a license fee is 
 the sum charged for such permit. 
 
 Duties or customs are taxes levied by the government on goods imported 
 from foreign countries. 
 
 An ad valorem duty is a tax levied upon imported goods at a certain per 
 cent of their dutiable value. 
 
 Duties are not computed on fractions of a dollar. If the cents are less than 60 
 they are rejected ; if 50 or more the dollars are increased by i. 
 
 A specific duty is a tax levied upon imported goods according to their weight 
 or metisure, and without reference to their value. 
 
 Some goods are subject to both a gpeciflc and an ad valorem duty. 
 
 PRACTICAL EXERCISES. 
 
 127. The assessed value of a property is $4760, and the rate 
 of taxation J % . Find the tax. 
 
 128. The assessed value of a house and lot is $7500, and the 
 rate of taxation J%. Find the tax. 
 
 129. My real estate is assessed at $8500. The rate is three 
 mills on the dollar. What taxes have I to pay if I am allowed 
 4% for prompt payment? 
 
 130. A -nan's property is assessed at $7200. What is his tax, 
 the rate being $8.75 on $1000? 
 
 131. The assessed valuation of a town is $3,500,000. The 
 money to be raised is $4,900. What is the rate? 
 
 132. What is ti e tax on 9350 pounds of tobacco at 16 cents ? 
 
TAXES. 127 
 
 133. A tax of 65900 is levied for building a school-house. The 
 assessed valuation of the village is $2,242,000. What is ' ae tax 
 on a property assessed at $6760 ? ' 
 
 134. A teacher pays an income tax of 3 mills on the dollar 
 
 ^o mfse tmt '^*' """'* ^'""^^'^^ '^''^""'^ ^* ^'^ ^^ ^'^'"^^ 
 
 * ^^?;2!o **^ '" *^^ valuation of a piece of property that pavs a 
 tax of 11273 at a rate of 3^ mills on the dollar ? ^ ^ 
 
 «->f(L^^ w"" 1*^^^^ ^' "''"''"^ "P"" ^ ^^"^^'^ "^i" valued at 
 
 ta; oTsSH 50 V^: "''"" "' ' P'^^' "' P^^P«^*y '"^^^ P-y« a 
 tax ot $38.50, at the same rate ? 
 
 138. What sum must be assessed on a school district to build 
 a school-house at a cost of $5460, and pay 2J % for collection ? 
 
 139. What sum must be raised in order that $19,600 shall re- 
 mam after paying a commission of 2% for collecting the taxes? 
 
 7ol^*tsT^'* '' *^' '*'' '''' ^^^^ ^^"^"' ^^ ^^^^^^^'i «Pi"t« «t 
 
 141. How much is the semi-annual tax of a national bank 
 
 l2r6 8roT.f"'f '" " ^''''''' ^* *^^' ^--^^ deposits 
 «^,cf4b,840 at i%, and average capital stock $800,000 at |%. 
 
 142. A pedlar pays a license fee of $12.50 per year His net 
 income for a certain year is $87.. The tax is equivalent to 
 what rate per cent ? 
 
 143. What is the duty, at 20%, on 420 boxes of raisins, each 
 contammg 40 pounds, and costing 7 cents a pound ? 
 
 144. A merchant's importation of silks from France was in- 
 
 rate being 60%. ' 
 
 146. Find the duty on a shipment of books from the United 
 ■states to Canada, invoiced at $.324.20, at 15%. 
 
128 
 
 FIITH DEPARTMENT. 
 
 146. Woolens valued at £423 128. 6d., and weighing 724 
 pounds, *vere imported from England. What was the duty at 
 40 cents per pound and 25 % ad valorem. 
 
 147. Find, in American currency, the duty on a shipment of 
 linens from Ireland, invoiced at £123 Ss. 6d. , at 35 % ? 
 
 148. What is the duty <m 4308 pounds of wool, invoiced at 
 $1826, when the rate is 7 cents per pound and 8 % ad valorem ? 
 
 149. Goods invoiced at $450 have become damaged. Find 
 the amount of the duty at 33J%, the allowance for damages 
 being 25%. 
 
 160. At 40% ad valorem, what is the duty — Americ cur- 
 rency — upon an importation of 300 dozen kid gloves, invoiced 
 at 72 francs per dozen ? 
 
 151. A Toronto fruit dealer imports 24 boxes of oranges from 
 Florida. Each box contains 260 oranges. They are invoiced at 
 $2.75 a box. The freight is $10.15, the duty 15%, the broker's 
 fee 60 cents, and the expense of delivery 75 cents. How much 
 will be gained by selling the oranges at 25 cents per dozen ? 
 
 VI. REVIEW. 
 
 MISCELLANEOUS DRILL EXERCISES. 
 
 152. Five per cent of a number is what per cent of J of the 
 number ? 
 
 153. By selling cashmere at $1.40 per yard I gain 16§%. 
 What is my gain en a sale amounting to $32 ? 
 
 154. A merchant's collector deducts his commission of 2% 
 from a bill ; the balanca is $1960. What was the bill ? 
 
 155. A merchant buys a quantity of coffee and sells it again 
 so as to gain 10%. Had he bought it at 10% less and soid it for 
 $5 less, he would have gained 20 % . Find the cost price. 
 
HEVIEW. 
 
 129 
 
 156. A dealer sells a horse at a loss of 4 % . Had he sold if 
 f- gumeas n.ore he would have gained 5%. FinS the o^tl} 
 
 167. A boy buy, chestnuta at »2.60 a bu.ho' an,I ..11. .1 
 «t 5 cent. „ pint. What per cent doe. he make » "'" 
 
 thereby S'ao"^'''.''^ " u """T""'"'^ '"W '' for »1200, 
 
 «er„„::r:rrzr:rdrf-r.^^^^^^ 
 
 160. A bookseller bought Christina- n„,.,ic *. j- 
 30% and 5% Th« .1 f"\^""«*'"a« cards at a discount of 
 
 deducted 3% Th\ I' n ''''"''' '"^ '"^^^^"8 ""^ the bill 
 
 the cards? '^^^*^ ^^'^^^^ ^'^ve been the cash price of 
 
 161. I bought G50 yards of silk in Paris at $5.25 a yard Th« 
 charge for freight was $15.40, and for storage «5 85 T • , 
 ad valorem duty of 25%, and sold the goorfot^STlC ' Whit 
 was my gain per cent ? ™r »0/10. What 
 
 162 In the erection of a bam I paid twice aa much for lumber 
 as for labor, and twice as much for labor as for stone hit 
 paid 8% „.ore for lumbar, 8% more for labor and 2^n,ofe1 
 stone, the^bam „„,a have cost me |3no. wllt l^ ^^JZ 
 
 fo "L"«c^::12?.^"orm^dtd';i!• " '"'" " ^ ^ 
 
 /f ■ iAow mucn did the carriage cost A ? 
 164. A grocer buys two sorts of tea at 2s 9d and %, 1J 
 pound respectively. He mixes them so as to have 3 pounds':, 
 
 46. per pound. What does he gain per cent ? 
 
 shouTd /Lif ir":"j r r^tif *^-»» ^ ■- «^- '- -ow much 
 
Mlpt 
 
 130 
 
 FIFTH DEPARTMENT. 
 
 I a 
 
 166. Two pors.jus coimnencod buBinc»B «ith ociual capital. 
 One gainod 25%, tlio other 33_^ %. What was their capital if the 
 difference between their gains is ^2720? 
 
 167. I send my agent $2075.70 to invest in sugar, after deduct- 
 ing his coinniission of 1|% of the sum invested. How many 
 pounds at 8i cents sliouid he forward ine 1 
 
 168. Two boys buy apples at a cent each. One sells them at 
 3 for 4 cents, and the other at 4 for 6 cents. Compare their 
 gains per cent. 
 
 169. A merchant sold two overcoats for equal sums of money. 
 He gained 25% on the one and lost 25% on the other. His loss 
 on the whole transactitm was $2.40. Find the cost of each coat. 
 
 170. An implement dealer asked for a reaper 30% more than 
 it cost. He finally took 20% less than ins asking price, and 
 gained $5 on the machine. How much did he ask ? 
 
 171. The proprietor of a factory projjoses to reduce wages 
 12^%. His men strike, but afterwards submit on condition that 
 their wages remain tlie same, but that their time, which is 10^ 
 liours a day, be increased. How much should it be increased ? 
 
 1 , 2. I Pold two horses and got 6^ % less for the second than 
 for the first. On the first I gained 20% and on the second 1 lost 
 10%. My whole gain was $15. Find the cost of each horse. 
 
 173. What must a merchant ask for boots that cost $3.60 a 
 pair that he may make a discount of iO% and still gain 26%? 
 
 174. A merchant's sales for one week showed an increase of 
 10% each day on the sales of the pievious day. His total sales 
 for the week amounted to $3857. 80|. Find his average sales 
 per day. 
 
 175. A grocer luys sugar at the rate of 12 pounds for $1 and 
 sells it at the rate of 10 pounds for $1. What does he gain per 
 cent ? 
 
 176. If I sell f of an article for what f of it cost me, what per 
 cent do I lose ? 
 
 I 
 
REVIKW. 
 
 131 
 
 He^Jn* ^ ^"';»""*'^''' P"''^ f'>r certain books is 25% above cost 
 He allows teacho-s a diaco.int of 12%. Ho receives « 4 f ! 
 teacher n. payment of a bill. What profit drrra^e? ' 
 
 co^ntiZo^ " the difference on a bill of 8875 between a di«. 
 coant of 40%, and a discount of 30% and 10%? 
 
 mlf\l "'"I'^ *"^r * '^""''^ "« *«" ^^' «*«1^ t"«hel ground 
 >vjiat per cent does he take for toll i K"'una, 
 
 180. Wliat per cent of ^\ is ^ ? 
 
 181. A girl who attended school 68 days durincr „ + 
 
 182. A horse and carriage were sold for SUM +. i 
 
 gain of 20 f/. ..n,i *^u • **^" t'le horse at a 
 
 ijd.in or j:v/o and th^ carriage at a loss of 10'/ tj i 
 
 I of what the carriage cost' ^JZ IIVLI'' '''''' '''' 
 
 oos?^ FtT'''"* !"r ''^^ ^^ ^^'""^° ^«-^« '' 75 cents below 
 coat. For liow much should he sell the goods to gain 10% 
 
 retailers make ? ^ ''"'^ ^''' '^^^ P^^«^ ^« the 
 
 186. At what price must a bookseller raark a book which costs 
 make' ^O^f ^ '''' '^ "^^^ ^^^^ ^' '"^^ ^« ^ «^"^ent and^H 
 
 187. A wholesale dealer sold at a profit of 25% to a retailer 
 who compromised with his creditors at 40 cents 1 he t "' 
 What per cent did the wholesale dealer lose ? 
 
 Jf\ ^ fr"' ""f ^""^ ^ ^"^""^y ^f *«^ ^* ^" advance of 20% 
 on cost. After selling f of it he reduced the price 8 cents a 
 
 he" It red ^' dif '"''• "" '''^ "' ^^^^ ^* ^"^^ W bee^L 
 he not reduced the price. What did the tea cost per pound ? 
 
 189. A broker charges ^,% for investing money, and receives 
 r a certain transanfmr, ©qu qo t7<- , , , / ' receives 
 
 JB for a certain transaction S.30.80. 
 
 r md the sum invested. 
 
l»ll. 
 
 li 
 
 
 
 I 
 
 132 
 
 FIFTH DEPARTMENT. 
 
 190. I bought two city lots for $450 and $300 respectively. I 
 sold both ftt the same price, and gained as much j)er cent on the 
 one as I lost on the other. What did I gain or lose per cent on 
 the transaction ? 
 
 191. An article is marked to gain 40%, but the seller throws 
 ofl' 10%. A collector is afterwards [>aid 20% of the debt for 
 collecting it. What per cent is gained i 
 
 192. I sold goods at a certain gain per cent. If they had cost 
 me 50 % less my gain would have been six times as great. What 
 per cent did 1 gain / 
 
 193. I marked goods to gain C0%, but (»n account of using an 
 incorrect yard measure I gain only 40%. What is the length of 
 the measure / 
 
 194. A dealer sells 20 pounds of tobacco at a profit of 5%, and 
 30 pt)und8 at a profit of 8%. If he had sold it all at a profit of 
 6% he would have received 20 cents less. What was the cost 
 per pound ( 
 
 195. A hatter's expenses during a certain year were 33J% of 
 1 1 is gross gain on merchandise. H is hats were marked .'iO % above 
 cost. At the beginning of the next year he advanced the price 
 of his ^roods 10% of the marked price, and during the year cut 
 down his expenses 10%. What did he gain per cent during the 
 second year 'I 
 
 196. A druggist purchases brandy at $4 a gallon, and adds 
 water so that when he sells it at $3 a gallon he clears 50%. 
 W hat per cent of each gallon of the mixture is water ? 
 
 197. I had a village lot worth $120; I sold it for $130; being 
 dissatisfied with my sale, I inniiediately bought the lot back for 
 $150. What did I lose i)er cent by the double transaction ? 
 
 198. An engine was sold for $3525, at a loss of G%. For how 
 much should it have been sold to gain 12|%. 
 
 199. If I compromise with an insolvent creditor for 70 cents 
 on the dollar, and then discount 2% for immediate payment, 
 what is my total loss on a claim of $6500 ? 
 
SIXTH ])EPARTMENT. 
 
 I. INTEREST. 
 
 HINTS AND DEFINITIONS. 
 Interest is the sum cfmr^'wl for the use of money 
 I.^erest is ro.lly the use of „u.u>y, or the benefit .le'rive.i from its uso 
 The principal is the sun, for the use of which interest is pal<l 
 Jr^ "te orinterest is the per cent of the principal charged for it, use for one 
 The amount is the sun. of the principal and interest 
 Legal intereat is the interest recked at the rate per cent fixed by law 
 Usury is interest at a higher than the legal rate. 
 Simple interest is interest „n the principal only, for the full time 
 
 EXERCISES FOR MENTAL DRILL. 
 NoTR.-l)o not use i>en or pencil. 
 
 of }l ^^ l^ 7o[' *"" '''""' ^""' "^"*^'' ^'^^"^^l b« P'"d for the use 
 of a boat for 12 hours ? 
 
 of a'cr? w,::;;' """ "-* *"""• - '"'- ""^>^ *^-' 
 
 a bit* ^tt'thV;'"""' """' "'"°" """"" "' """^^"^ * ~ »' 
 
 6. At 16 a year how much should be paid for the me of MOO 
 o jr ©ftrs ' 
 
 6. A man hires a horse for 3 hours at |tl.50 an hour. What 
 wui Ills tivery aire amount to ? 
 
.''•»•: 
 
 134 
 
 SIXTH DEPARTMENT. 
 
 7. A man rents a house for 13 months at $12 a montli. Wliat 
 will his rent amount to ? 
 
 8. A man borrows $600 for 1 year at $7.50 a hundred. How 
 much interest will he have to pay ? 
 
 9. A man borrows $400 for 3 years at $6 a hundred a year 
 (6%). How much will he have to pay /or its use ? 
 
 10. VVhat is the interest of $500 for 4 years at 6%? 
 
 BUSINESS EXERCISES. 
 
 Direction.— The principal, the time, and the rate are given ; it is required to 
 find the interest. 
 
 11. Principal, $200. Time, 2 years. Rate, 6%. 
 
 12. T'rmcipal, $340. Time, 3 years. Rate, 7%. 
 
 13. Principal, $420. Time, 4 years. Rate, 4%. 
 
 14. Principal, $720. Time, 5 years. Rate, 3%. 
 
 15. Principal, $844. Time, 1^ years. Rate, 6%. 
 
 16. Principal, $933. Time, | year. Rate, 5J%. 
 
 17. Principal, $225. Time, § year. Rate, 4^%. 
 
 18. Principal, $862. Time, 2i years. Rate, 3^%. 
 
 19. Principal, $1000. Time, 3 years. Rate, 7%. 
 
 20. Principal, $1200. Time, 5 years. Rate, 4%. 
 
 21. Principal, $3200. Time, 3 months. Rate, 8%. 
 
 22. Principal, $4850. Time, 9 months. Rate, 6%. 
 
 23. Principal, $2030. Time, 6 months. Rate, 2|%. 
 
 24. Principal, $1425.30. Time, 3 years. Rate, 6%, 
 
 25. Principal, $1267.50. Time, 6 years. Rate, 7%. 
 
 26. Principal, $2102.30. Time, 1 year. Rate, 3%. 
 
 27. Principal, $4215.50. Time, 1 year -^ months. Rate, 2%. 
 
 28. Principal, $3984. 27. Time, 2 years 9 months. Rate, 2^ % , 
 
INTEREST. 
 
 135 
 
 D.KKc™.v.-l„ the exercise. ^'^l^'^^^^^^^^^^Z^^^^^^ 
 
 29. What is the interest of $240 from JunP S isftr * a 
 
 3, 1887, at (i%i "*- ^' ^^^^' *" August 
 
 30. What is the interest of 11425.80 from September 15 l««fi 
 to November 15, 188G, at 2%? ' ^^^^' 
 
 31. What is the interest of $125.50 from May 15 1885 to 
 Decembei- 15, 1887, at 4%? ^ ' ^^^' *" 
 
 32. Wiiat is the interest of $480.40 from .Tune 18 ISS^ * 
 August 18, 1884, at 5r^? ^' ^^^'^' *« 
 
 ana divide the prc^uctbTsS "'""' '''" °"^ ^'^^^ ^^^ ^^e number of d„j.« 
 
 33. Principal, $420. Rate, 4%. Time, 73 clays. 
 
 34. Principal, $663. Rate, 2%. Time, 48 days. 
 
 35. Principal, $360. Rate, 8%. Time, 33 days. 
 
 36. Principal, $840. Rate, 7%. Time, 33 days. 
 
 37. Principal, $1200. Rate, 2%. Time, 146 days. 
 
 38. Principal, $1425.20. Rate, 3%. Time, 219 days 
 
 39. Principal, $3268.60. Rate, 6%. Time, 132 days. 
 
 40. Principal, $4232.50. Rate, 8%. Time, 100 days 
 
 41. Principal, $1008.20. Rate, 7%. Time, 203 days. 
 
 42. Prin.,$1200. Rate,3%. Time,Jan. 3, 1886, to Mar. 15,1886 
 
 43. Prin.,$1420. Rate,4%. Ti„,e,D.,,-. 5,1886,to Apr. 18,1887" 
 
 44. Prin.,$1730. Rate,5%. Time, Nov. 9, 1886, to May 27 1887 
 
 45. Prin.,$2190. Rate,2i%. Time,Sept.4,1885,to July 19,1888 
 
 46. Prin.,$4380. Rate,3i%. Time,Dec. 3,1885,toMar.21.1887 
 
 47. Prin.,$3625. Rate.Uf.. Time, Oct. 2,i38b,toMay 17 1887 
 
136 
 
 SIXTH DEPARTMENT. 
 
 SIXTY-DAY METHOD. 
 
 Note. -Consider 360 days one year, and 30 days one month ; then the interest 
 for 60 days, or two months, at any rate, will be i of the interest for one year ; and 
 when the rate is 6% the interest for 60 days is 1% or jJo of the principal. 
 
 Illustrative Exercises. 
 1. What is the interest of ^1728 for 80 days at 6%? 
 
 The interest of 81728 for 60 days at 6% 
 is 1% of $1728, or *17.28 ; and the interest 
 for 20 days (i of 60) is i of !iil7.28, or #5.76. 
 Hence for 80 days it will be .§17.28 plus 
 $5.70, or«23.04. 
 
 5 
 
 $23 
 
 28 = interest for 60 days. 
 76 = interest for 20 days. 
 
 04 = interest for 80 days. 
 
 2. What is the interest of $1260 for 106 days at 6%? 
 
 112 
 6 
 2 
 1 
 
 60 = interest for 60 days. 
 30 = interest for 30 days. 
 10 = interest for 10 flays. 
 26 = interest for 6 days. 
 
 Cut oflF two places to the right, 
 iof $!12.60 = S6.30. 
 Jof^.30=«i2.10. 
 iof«6.30=«1.26. 
 
 $22 i 26 = interest for 106 days. 
 
 Note.— Any number of days can be divided into convenient parts. Thus, to find 
 the interest for 158 days, we could take twice 60 or 120 ; then 30, which is i of 60 ; 
 then 5, which is i of 30 ; then 3, which is i\, of 30. 
 
 m 
 
 3. What is the interest of $2340 for 3 months 27 days at 7%? 
 
 $23 
 
 11 
 
 7 
 
 2 
 
 $45 
 7 
 
 $53 
 
 40 = interest for 60 days or 2 months. 
 70 = interest for 30 days or 1 month. 
 80= interest for 20 days. i of 823.40=«t7.80. 
 34 = interest for 6 days. J of $11.70=^.34. 
 39 = interest for 1 day. J of $2.35= .39. 
 
 63 = interest for given time at 6 % . 
 61 = interest for given time at 1 %. 
 
 i of $45.63 =$7.61. 
 
 25 = interest for given time at 7 % . 
 
 Note.— Add 1 cent when the fraction is J or more. 
 
INTEREST. 
 
 137 
 
 4. What is the interest of ^600 for 5 months 19 days at 4%? 
 $36 00 = int€re8tfor60daysor2month8. 
 
 18 
 
 90 
 9 
 1 
 
 $101 
 33 
 
 $67 
 
 00 = interest for 1 month 
 
 00 = interest for 5 months. 
 00 = interest for 15 days. 
 80= interest for 3 days. 
 60 = interest for 1 day. 
 
 40 = interest for given time at 6%, 
 80 = interest for given time at 2%. 
 
 60 = interest for given time at 4%. 
 
 818.00X 5=100.00. 
 
 15 = iof60. i of 136.00=19.00. 
 
 J of ^.00=«I1.80. 
 
 iof fl.80= .60. 
 
 3 = iof 15. 
 l = iof 3. 
 
 Take i of «il01.40 from itself. 
 
 BUSINESS EXERCISES. 
 DiRECTiON.-Find the interest by the slxty-day method. 
 
 48. Principal, $245. Rate, 6%. Time, 18 days. 
 
 49. Principal, $368. Rate, 6%. Time, 14 days. 
 
 60. Principal, $725. Rate, 6%. Time, 15 days. 
 
 61. Principal, $463. Rate, 6% 
 
 62. Principal, $842. Rate, 6%, 
 ■ 63. Principal, $520. Rate, 6%, 
 
 64. Principal, $368. Rate, 6%. 
 
 65. Principal, $863. Rate, 6%. 
 
 66. Principal, $721. Rate, 7%. 
 57. Principal, $484. Rate, 7%. Time, 69 days. 
 88. Principal, $285. Rate, 7%. Time, 73 days. 
 
 59. Principal, $393. Rate, 5%. Time, 86 days. 
 
 60. Principal, $685. Rate, 5%. Time, 89 days. 
 
 61. Principal, $268. Rate, 4%. Time, 95 days. 
 
 62. Principal, $936. Rate, 8%. Time, 99 days. 
 
 Time, 16 days. 
 Time, 19 days. 
 Time, 27 days. 
 Time, 33 days. 
 Time, 37 days. 
 Time, 48 days. 
 
 ■ 
 
II 
 
 Id^ 
 
 SIXTH DEPARTMENT. 
 
 
 63. Principal, $6000. Rate, 9%. Time, 147 days. 
 
 64. Principal, ^800. Rate, 5%. Time, 201 days. 
 66. Principal, $1233.45. Rate, Ofo. Time, 127 days. 
 
 66. Principal, $8426.30. Rate, 6%. Time, 132 days. 
 
 67. Principal, $9635.25. Rate, 6%. Time, 143 days. 
 
 68. Principal, $7628.35. Rate, 6%. Time, 214 days. 
 
 69. Principal, $8428.13. Rate, 7%. Time, 121 days. 
 
 70. Principal, $6213.40. Rate, 8%. Time, 129 days. 
 
 71. Principal, $2468.20. Rate, 4%. Time, 184 days. 
 
 72. Principal, $3564.90. Rate, 3%. Time, 163 days. 
 
 73. Principal, $2104.85. Rate, 2%. Time, 319 days. 
 
 74. Principal, $6812.24. Rate, 10%. Time, 119 days. 
 76. Principal, $3154.62. Rate, 12%. Time, 133 days. 
 
 76. Principal, $1009.40. Rate, 11%. Time, 148 days. 
 
 77. Principal, $1263.84. Rate, 13%. Time, 101 days. 
 
 NoTE--The interest for years and months is found by the sixtv-dav method h,r 
 multip^m, the interest for 60 days, or two months, ify one haff Z number of 
 
 78. Principal, $1240. Time, 9 mo. 27 da. Rate, 3%. 
 
 79. Principal, $3964. Time, 4 mo. 24 da. Rate, 2^^/,. 
 
 80. Principal, $6280. Time, 7 mo. 13 da. Rate, ^%. 
 
 81. Principal, $3630. Time, 6 mo. 22 da. Rate, 5^%. 
 
 82. Principal, $1248. Time, 5 mo. 14 da. Rate, 1|%. 
 
 83. Principal, $1850. Time, 8 mo. 26 da. Rate, 2^%. 
 
 84. Principal, $4253. Time, 1 yr. 3 mo. 19 da. Rate, 7%. 
 86. Principal, $5631. Time, 2 yr. 5 mo. 25 da. Rate, 8%. 
 
 86. Principal, $4280. Time, 3 yr. 7 mo. 18 da. Rate, 10%. 
 
 87. Principal, $3216. Time, 4 yr. 10 mo. 29 da. Rate, 2^%. 
 
INTEREST. 
 
 139 
 
 88. Prin.,i75.63. Rate, 2%. Time, Apr. 3, 1886, to Jan. 19,1888. 
 
 89. Prin.,$42.85. Rate, 3%. Time, May 7, 1886, to Dec. 30,1887. 
 
 90. Prin., $95.43. Rate,6%. Time, Mar. 8, 1886, to Nov. 18, 1886. 
 
 91. Prin., $27. 68. Rate,|%. Time, July 5, 1885, to Feb. 22,1887.' 
 
 92. Prin., $71.15. Rate,l%. Time, May 6, 1885, to Aug. 21, 1887. 
 
 93. Prin., $39. 60. Rate,i%. Time, July 1, 1885, to Sept. 30, 1887. 
 
 NOTE.-In many examples labor can be saved by havintr the time and nrin 
 
 tnfrr'^'T- '''"^' •"^*^^'^ «' «"'^'"^' the'interest^ r^eonorlSoC" 
 find the interest of «139 for 60O days. The results will be identical. ^ ' 
 
 94. Find the interest of $600 for 139 days at 6%. 
 
 95. Find the interest of $120 for 97 days at 7%. 
 
 96. Find the interest of $300 for 219 days at 4 % . 
 
 97. Find the interest of $400 for 185 days at 3%. 
 
 98. Find the interest of $180 for 187 days at 2%. 
 
 99. Find the interest of $240 for 287 days at 8%. • 
 
 WRITTEN DRILL EXERCISES. 
 DiRECTiON.-Find the accurate interest except where otherwise directed. 
 
 100. Find the amount of $425 for 16 months at 7%. 
 
 101. Find the amount of $1200 for 1 year 9 months at 8%. 
 
 102. What is a banker's gain in 2 years on $12,000 deposited 
 at 5% and loaned 22 times at 1|% a month ? 
 
 ■ l^^* t "'■'''' ^'''■'''''^' ^^^^^ ^^ ^^" ^"^ 1^^^^« i* immediately at 
 •2 %. What does he gain in 9 months ? 
 
 104. A man invested $2400 in a publishing business, and at 
 the end of 2\ years he withdrew $2940, being investment and 
 prohts. What annual rate of interest did his investment pay ? 
 
ii 
 
 tlfe»«;iKa.-*RS 
 
 140 
 
 SIXTH DEPARTMENV. 
 
 
 >'P !H 
 
 105. Find the 
 
 $453. 
 
 amount 
 June 13, 1887, at 9%. (Sixty-day mothod.)" 
 
 106. A man pays $375 a year rent for a house wortli $6400. 
 Will he gain or lose, and how much in 4 years, if he borrows 
 money at 7 % to purchase the house ? 
 
 107. Bought a piece of property for $3000 and agreed to pay 
 for It in 8 months with interest at 8%. What amount will be 
 due at the expiration of tlie time ? 
 
 108. What nnist be paid f,)r a loan of $1800 for 3h months 
 at 1^ % a month ? 
 
 109. A merchant charges 1% a month on over-duo accounts. 
 How much should he collect for an account of $428.30 which is 
 7 morths over-due ? 
 
 110. A man invests $9040 so that it yields him an annual 
 income of $1156.80. What is the rate of interest ? 
 
 111. At what rate per annum will any sum double itself in 5 
 years ? 
 
 112. What is the rate cf interest when $7500 yields an income 
 of $02.50 a month? 
 
 ^ 113. In what time will any sum of money double itself at 
 
 114. The half-yearly interest on a mortgage at 7% is $386. 
 What is the face of the mortgage ? 
 
 115. A boy is now 17 years old. How much must be invested 
 ft)r him at 7%, simple interest, that when he is 21 he mav 
 have $64,000? ^ 
 
 </^ 116. At what ratt; will the interest of $652 for 16 years be ^f") • 
 $440.10? ^ ^ < u 
 
 y 117. In what time will $230 amount to $391 at 7 % ? ... 
 
 ^ 118. What sum will amount to $2050 in 8 months at 9 % ? o i- ^ 
 
 119. The interest of a sum of money for 11 years at 3^% is 
 $77. What is the sum ? ' " •. 
 
>, 1886, to 
 
 rth $5400. 
 e borrows 
 
 od to pay 
 nt will be 
 
 \ months, 
 
 accounts. 
 ) which is 
 
 in annual 
 
 itself in 5 
 
 n income 
 
 itself at 
 
 is $386. 
 
 invested 
 he may 
 
 years be ^' /.• 
 
 10 
 
 b 3^% is. 
 
 • INTEUEST. 2^1 
 
 ' hoi^" ^ '"'" "^ "n""^ "'""""*" '" ^ y""''^ '^* 11% to #o!)7. In 
 how many years will it amount to $(J(j3? -fr" <• m 
 
 121. The interest of $I4<;0 for one day is 25 cents. Find the 
 rate per cent per annum ? ^"** 
 
 vvas rf of the sum itself. What rate per cent was charge.l ( 
 
 i.it oli^2(;;;'r '^"'"^ '"'^"^* '^^ '^^ ^'" ^^^^^ - ---^ 
 
 126. A house which cost $4800 rents for #24 a month What 
 IB the net rate per annum of interest received on the investmen 
 if the average annual expense is $48 i "Htstment 
 
 me^l?32.to h". "t"''' ' """'^^ "'^""^'^ ^ ''''' '' ^'^'"«° ^'"^^ costs 
 rpetdtiV ' ''''' "^^^" ''' ^''' '-""•" "i- ^^« -- 
 
 teS ^'"'' '"'" '" ^"^ '""""'' *^' ^^^^ ^"^ P^'"^"«^' «3.0(i in- 
 
 kJ of imon^^^i r'" "' ^ "'""'^'' '^^ '^^^ ^^" '^"^^^""t to the interest CT . 
 y^ of $1000 for 13 years at 4 % ? it^iesc^ ^_ ^^ 
 
 ,1^®;/" ^''''* ^""^^ "* «""P^« interest will $723.10* return * 
 of Itself in interest at 7^ % ? \ ^ ^ 
 
 130. A certain sum in 8 months am\unts to $790 and in 10 
 s/ months to $845. What is the sum andke rate per cent ? 
 
 131. What is the value of a house if a rental of $15 a month 
 IS equivalent to 7^ % on the value ? 
 
 132. A merchant who clears 15% annually on his investment 
 IS forced by poor health to give up his business and to lend h"s 
 money at 0^%. His income is thus reduced $2,550. Find his 
 mvestment. " 
 
 J^^f:J^l'''1"""' "^\ " *'''*^"'" «""^ "^ ^ y-^rs is § of itself. 
 
mm 
 
 142 
 
 SIXTH DEPARTMENT. 
 
 EXERCISES IN COMPOUND INTEREST, 
 llluatratlve Exercite. 
 Find the compound interest of $1000 for 3 years at 4%. 
 
 FIRST METHOD. 
 
 $1000.00 Prindpal. 
 
 40.00 Interest for 1 year. 
 
 $1040.00 Amount for 1 year, or second principal. 
 41 .60 Interest for 1 year. 
 
 $1081 .60 Amount for 2 years, or third principal. 
 43. 26 Interest for 1 year. 
 
 $1 124.80 Amount for 3 years. 
 1000.00 Original principal. 
 
 $124.86 Compound interest for 3 years. 
 
 SECOND METHOD. 
 
 Amount of $1 for 1 year at 4% -$1.04. 
 Amount of $1 for 3 years at 4% =$(1.04)''. 
 $(1.04)='=$(1.04x 1.04x1.04) = $!. 124864. 
 Amount of $1000 = .|( 1000 x 1.124864) = $! 124.86. 
 Compound interest=|1124.86-$1000 = $124.86. 
 
 NOTB,— If the interest is compounded semi-annually the rate per cent is one- 
 half of the yearly rate ; if quarterly, one-fourth of the yearly rate. 
 
 134. Find the compound interest of $1000 for 3 years at 6%. 
 
 135. Find the compound interest of $1200 for 2 years at 7% 
 
 136. Find the compound interest of $2000 for 4 years at 2%. 
 
 137. Find the compound interest of $5000 for 3 years at 5%. 
 
 138. Find the compound interest of $8200 for 2 years at 4%. 
 
INTEREST. 
 
 143 
 
 <'^n'lZZ'^2t^^^^^^^ "^ '^f'^ «' >•«- -<^ -onths. fl„d the 
 
 at 3^% : ^'""^ ^^'" ««'"P'^""d interest of ^50 for 2 years G months ^'>/ ^. 
 
 at IT" ^""^ *''^ ^«"^P«""d interest of J|120 for 3 years 3 months 
 
 at n'. ^'""^ *^'' «""^P°"^d interest of 8840 for 2 years 9 niontlis 
 
 J'^yXr"'''"^'---''^ '^ ' years/compoundedan- 
 
 anf i,;ii: w" ''''' ^"^"""^ *^ '^ ' ^^^^^' --^-"^^^ -"^- 
 
 145. If, at tlie age of 25 years, a person places $1000 on in- 
 terest, conjpounded annually at 6%, wliat will be the amoi.nt 
 due him when he is 50 years old ? (1.06^ = 4.2919). 
 
 146. A father deposits HlOO in a savings bank when his child 
 1 year old How much will this amount to when the c d 
 
 (il^Zmi "^''"' ''"' ""'""'^' semi-annually at 4%1 
 
 148. How much should a father invest at 5% compound in- 
 terest for his son who is 3 years old so that when he comes f 
 age he may have $10,000 ? (1.05>« = 2.4066). 
 
 149. Find the difference between the compound and simnlp 
 interest of $3000 for 3 years at 7|%. ^ 
 
 160. What is the interest of $3000 for 12 years at 4% per 
 annum, compounded quarterly ? (1.01<« = 1.6122.) 
 
 allilVinl""^ ^n.T^'T '^ ^^^ ^" ^^ ^''^''' compounded annu- 
 ally at 10 % . (1 . 165 == 239 0591 . ) 
 
 /^ 
 
 H 
 
144 
 
 SIXTH DEPARTMENT. 
 
 II. COMMERCIAL PAPER. 
 
 Commercial paper embraces notea, checks, drafts, bills of 
 exchange, etc. 
 
 A note is a written promise to pay a specified sum ai' p. certain 
 time. 
 
 The person who promues is called the maker, and the person, 
 to whom he promises is called the payee. 
 
 The face of a note is the sum of money promised. 
 
 A negotiable note is one which is made payable to the 
 bearer, or to the order of the payee. A negotiable note can be 
 sold or transfered. 
 
 A note is non-negotiable when it is payable only to the 
 person or persons named in the note. 
 
 A draft is a written order by one person on another for the 
 payment of a specified sum. Drafts on foreign countries are 
 called bills of exchmuje. 
 
 A bank draft is a written order by one bank on another for 
 the payment of a specified sum to a person named therein, or to. 
 his order. 
 
 Drafts are made payable at sight, on demand, or at a ce- taini 
 time after date or after sight. 
 
 A bank check is a draft on a banking house, or on a bank,, 
 and is usually presented for payment. 
 
 Checks are not considered as actual payment until they are 
 paid, but in the course of business are regarded as cash. 
 
 Sight drafts, like checks, are presented for payment. 
 
 Drafts drawn on time are first presented for acceptance. 
 
 The person to whom the draft is presented ac-epts it by writing 
 across the face the word "Accepted," with the date, over his 
 signature. 
 
COMMERCfAL PAPEH. 
 
 Ho 
 
 A„ indorsement in blank i, .imply tho .iK„ature of .».. 
 '..d„rs„.. wntta, aor„« the back of the note or dmft 
 
 mt .ut fmther mdor,oment to any person holding it. ^ 
 • .le or draft i» indorsed in fUll when the indor,er state. 
 
 no" oTd^t h:;^z " wZ'nt': '""""""" '"^ '""'^"'™' °' ■^ 
 
 indorsing. """ '"""""'^ ">'«■• l"" "a™ when 
 
 ment or acceptance and wa, refused. "^ '°'' P"^" 
 
 The day of maturity is the day on which a note becomes due 
 
 MISCELLANEOUS HINTS. 
 The words used to make paper negotiable are order and bearer 
 The date means the day, rno,ith, and year 
 
 A note „,ay be written on any paper with ink or with pencil, and it will be good 
 A note made on Sunday is void. * 
 
 Notes bear interest only when so stated, except after maturity 
 If no time of payment is mentioned in a note it is payable on demand. 
 
 apS:rrL:Sr:.Sri: ^'^"" -'-^ -- P— -»>ose name 
 
146 
 
 SIXTH DEPARTMENT. 
 
 "Value received " need not necessarily be inserted in negotiable paper, but it is 
 desirable for the holder. , 
 
 Notes obtained by fraud cannot be collected. 
 
 A note made by a person while intoxicated cannot be collected. 
 
 The maker of a note is liable to any person who becomes the owner. 
 
 A demand note is valid until presented. 
 
 The amount is usually stated in both writin{f and figures. 
 
 When abank stamps or "certifies" a check it becomes responsible for the amount. 
 
 A bank cannot charge payment of a forged check to the one whose name was 
 forged to it. 
 
 Checks should be presented for payment within a reasonable time. 
 
 A draft on two persons who are partners need be presented to but one of them. 
 
 A draft does not bind anyone until it is accepted. 
 
 Each indorser, by his act in indorsing, certifies to the genuineness of each pre- 
 vious inuorsement. 
 
 A due bill is an acknowledgment and evidence of debt. 
 
 Ignorance of law does not excuse any person. 
 
 No contract is good unless there be a consideration. 
 
 Usually the name of a firm may be signed by any one of the partners. 
 
 When the day of maturity falls on Sunday, or on a holiday, the note is payable 
 on the day follov/ing. 
 
 If an indorser pays a note he can afterwards negotiate or transfer it. 
 
 Keleasing a prior indorser releases all who follow. 
 
 FORMS OF COMMERCIAL PAPER. 
 No. I. 
 
 1400. Pliiladelphia, Pa. , May 3, 1886. 
 
 Due iS. L. Clemens, or order, for value received, 
 
 Four Hundred Dollars. 
 
 R. J, Burdette. 
 
 v,t< 
 
 The above is a due bill payable ir money. It is one of the simplest fonns of 
 negotiable papers. If S. L. Clemens wishes to transfer this bill to some one else he 
 writes his name across the back of it. The third party can then hold both Clemens 
 and Burdette resposible. If payment is to be made in goods the words "payable 
 in goods from my store, on demand," or something similar, should be inserted. 
 
COMMERCIAL PAPER. 
 
 $200. 
 
 Two years 
 
 Rochester, N.Y., March 15, mo. 
 
 Charles' Dudley W^er ^^*'' ^"'^^ ^ ^''''^^' *" P^^^ 
 
 Two Hnndred -— -^HZT^ ~~ ^^ ^^^^^' 
 
 Dollars. 
 
 Value received. 
 
 E. P. Roe. 
 
 tt Will draw interest at the le.al rate uZ pa.U ''' '''^' "''''' "°* P-'^ ^^en 
 
 No. 3. 
 
 ffiOOK • 
 
 T'^^^nto* Onfc., January 3, 1886. 
 
 Two Hundred and Twenty-Five ~ ~~ ^^ be ^.^^ 
 
 „j. 4.1.- T .,_ . •' JJollars, 
 
 at the Imperial Bank. 
 
 Value received. 
 
 Nicholas Nickkhy. 
 
 No. 4. 
 
 $320.50. rj^.x ,, ~ 
 
 Boston, Mass., August 3, 1886 
 
 to IZ 7"''"^'*^^ •^^^^ -« J-ntly and severally promise 
 to pay Perry Mason rfc Co Promise 
 
 Three Hrcndred and Tweedy ^SZII^'I^V^'^' 
 with interest at 7%. Value received. ~~ ^^^^ ^^"^^«' 
 
 /o/m Greenleaf fVhittier. 
 '^(^'frff's Eussell Lowell. 
 
 cate at 7% per annum. ' *°^^'' ^' ^'"^ '^'^^s '"teiast from its 
 
If ( 
 
 148 
 
 SIXTH IjEPARTMENT. 
 
 No. 6. 
 
 . Nashville, Tenn., June 12, 18S6. 
 pay to the order of 
 
 1120. 
 
 At sight 
 
 Guy Mannering 
 
 One Hundred and Txoenty 
 
 value received, and charge to account of 
 
 Dollars, 
 
 To Adam Bede, 
 
 Jefferson City, Mo. 
 
 William Bobbin. 
 
 This draft is to be paid or cashed when presented. It must be indorsed pre- 
 viously by Guy Mannering. 
 
 No. 6. 
 
 $240. Chicago, 111., December 9, 1886. 
 
 At thirty days' sight pay to the order of 
 
 Will Carleton 
 
 Dollars, 
 
 Two Hundred and Forty 
 
 value received, and charge to account of 
 
 To Walt Whitman, 
 
 Cincinnati, Ohio. 
 
 Bret Harte. 
 
 This draft must be presented to Walt Whitman, for acceptance, by Will Carleton 
 or his agent. Whitman accepts the draft by writing across the face the word 
 " Accepted," with the date and his signature. When accepted the draft becomes a 
 note, payable 30 days after the date of acceptance. Drafts are sometimes drawn a. 
 certain number of days after date. 
 
 No. 7. 
 
 No. Milwaukee, Wis. , August 5, 19)86. 
 
 THE FIRST NATIONAL BANK 
 
 Pay Henry Ward Beecher, or order, 
 
 One Hundred Dollars. 
 
 T. DeWitt TalwMge. 
 
 This check must be indorsed by Beecher before being presented for payment. 
 Banks generally require checks to be indorsed, whether they are payable to order 
 or bearer. 
 
COMMERCIAL PAPFR. 
 
 149 
 
 EXERCISES IN TIME. 
 
 Of ^gZT^T^l^Io^:: ''^r" ir """*^« '^^■'^°" «-«» 'no"t^«. and add 3 days 
 dat^f Lturit, " '"' *'^ """ "^ «^^^"- " '« -''"'-'^ to find the 
 
 152. Jan. 5. Time, 3 mo. 
 
 .33. Feb. 3. Time, 6 mo. 
 
 154. Dec. 7. Time, 4 mo. 
 
 155. Nov. 9. Time, 2 mo. 
 
 156. Sept. 3. Time, 3 mo. 
 
 157. Oct. 10. Time, 9 mo. 
 
 158. Jan. 8. Time, 6 mo. 
 
 159. Sept. 7. Time, 6 mo. 
 
 160. Nov. 9. Time, 8 mo. 
 
 161. Dec. 1. Time, 5 mo. 
 
 162. July 15. Time, 9 mo. 
 
 163. May 23. Time, 8 mo. 
 
 164. June 27. Time, 4 mo. 
 
 165. Apr. 15. Time, 3 mo. 
 
 166. Mar. 22. Time, 2 mo. 
 
 167. May 20. Time, 4 mo. 
 
 168. June 18. Time, 5 mo. 
 
 169. July 29. Time, 10 mo. 
 
 170. Apr. 30. Time, 11 mo. 
 
 171. May 30. Time, 13 mo. 
 
 NoTE.-When the time is given in days the exact davs are 
 3 days of grace. The date of the note and time are given, 
 the date of maturity. 
 
 172. Sept. 12. Time, 15 days. 
 
 173. Nov. 23. Time, 20 days. 
 
 174. Dec. 24. Time, 30 days. 
 176. Jan. 18. Time, 35 days. 
 
 176. Aug. 19. Time, 45 days. 
 
 177. Mar. 30. Time, GO days. 
 
 178. Oct. 21. Time, 18 days. 
 
 179. Nov. 13. Time, 40 days. 
 
 180. Feb, 10. Time, 10 days. 
 
 181. Mar. 19, Time 30 da"? 
 
 182. July 3. 
 
 183. June 4. 
 
 184. Apr. 9. 
 
 185. May 3. 
 
 186. Mar. 3. 
 
 187. May 9. 
 
 188. June 7. 
 
 189. July 8. 
 
 190. May 9. 
 
 •tnt T >- 
 
 i.«7j.. <iune o. 
 
 to be reckoned. Add 
 It is required to find 
 
 Time, 60 days. 
 
 Time, 90 days. 
 
 Time, 70 days. 
 
 Time, 65 days. 
 Time, 45 days. 
 Time, 85 days. 
 Time, 47 days. 
 Time, 35 days. 
 Time, 90 days. 
 Tiiue, 20 days 
 
^'-'-mtm-xist^ 
 
 150 
 
 SIXTH DEPARtMENT. 
 
 tr 
 
 \i 
 
 NoTg.-When the year is not given consider February as having 28 days. The 
 date of the note and the time are given. It is required to find the number of day* 
 to maturity. 
 
 192. Jan, 23. Time, 2 mo. 
 
 193. Feb. 28. Time, 3 mo. 
 
 194. Mar. 30. Time, 4 mo. 
 
 195. Sept. 18. Time, 5 mo. 
 
 196. Oct. 20. Time, 6 mo. 
 
 197. Dec. 19. Time, 3 mo. 
 
 198. July 4. Time, 10 mo. 
 
 199. June 5. Time, 13 mo. 
 
 200. May 9. Time, 15 mo. 
 
 201. Apr. 8. Time, 18 mo. 
 
 202. Mar. 5. Time, 14 mo. 
 
 203. July 3. Time, 20 mo. 
 
 EXAMINATION QUESTIONS. 
 
 1. Explain the terms : vegotiahle, indorser, acceptance, protest. 
 
 2. When is-a note or draft non-negotiable ? 
 
 3. Distinguish between the words or bearer and or order. 
 
 4. How does a sight draft differ from a check ? 
 
 5. Is it necessary that a note be protested when payment is 
 refused '( 
 
 G. If a note falls due on Sunday when is it legally due ? 
 
 7. What does a time draft become when it is accepted ? 
 
 8. What will E. P. Roe have to do to make Note No. 2 pay- 
 able to the order of J. T. Trowbridge ? 
 
 9. Is note No. 3 transferable without indorsement ? 
 
 10. Why are the words "value received " inserted in notes ? 
 
 11. Write a check to draw money from your account in the 
 bank. 
 
 12. Can paper be transfered after maturity ? 
 
 13. What is meant by accommodation papur ? 
 
 14. What does an indorser do by his act ? 
 
 15. Is the maker of a note bound to pay if demand is not 
 made on the day of maturity ? 
 
 16. When is a note due if dated January 31 and made at one 
 month ? 
 
 a- 
 
BANK DISCOUNT. 
 
 151 
 
 III. BANK DISCOUNT. 
 
 HINTS AND DEFINITIONS. 
 
 Most note, discoiinM al bank, do not drew inlore.t. 
 
 The time in tiafk dimtunt is always the nnmli..p nf ,i^, > 
 »« ;™,, to the d„,e „/ „„„,;„. ' ' "°'"'"-' "' "•" "»" "■« "«'« «/ d»- 
 
 EXERCISES IN TIME 
 
 204. Date of note, Jau. 18. Time, 3 mo. DiscountedJan. 18 
 
 206. Date of note, Nov. 21. Time, 4 mo. Discounted Nov. 21. 
 
 206. Date of note, Dee. 13. Time, 5 mo. DiscountedJan. 13. 
 
 207. Date of note, Mar. 14. Time, 2 mo. Discounted Mar. 18. 
 
 208. Date of note, Aug. 22. Time, 3 mo. Discounted Sept. 14. 
 
 209. Date of note, May 30. Time, 30 da. Discounted June 15. 
 
 210. Date of note, Jan. 28. Time, 30 da. DiscountedJan. 31. 
 
 211. Date of note, Nov. 14. Time, GO da. Discounted Nov. 20. 
 
 212. Date of note, July 12. Time, 45 da. Discounted July 20. 
 
 213. Date of note, Sent 19. Time, 90 da. Discounted Oct. 10. 
 
r 
 
 162 
 
 SIXTH DEPARTMENT. 
 
 BUSINESS EXERCISES. 
 Illustrative Exercises 
 
 1. A note of $250, dated July 7, payable in GO days, is dis- 
 counted July 7 at 6 % ; find the proceeds. 
 
 This note is due in G.3 days, or Septenil)er 8. 
 
 The accurate interest of $250 for 0.3 days at 6% is $2.59. 
 
 The proceeds, then, will be $250 - $2.59, or $247.41. 
 
 2. A note of $730, dated August 3, payable in 3 months, is 
 discounted September 15 at 7 % ; find the proceeds. 
 
 The date of maturity is November 6. 
 
 The note then has to run, or is held by the bank, from Sep- 
 tember 16 to November 6, or 52 days. 
 The accurate interest of $7.30 for 52 days at 7 % is $7.28. 
 The proceeds, then, will be $730 -$7.28, or $722.72. 
 
 DiRECTiON.-Find the proceeds of tlie following notes. Compute the discount 
 on the basis of both 300 and 305 days to the year. 
 
 214. Face, $340. Time, 3 months. Rate of discount, G%. 
 Date of note, March 13. Date of discount, :March 13. 
 
 215. Face, $400. Time, 4 months. Rate of discount, 0%. 
 Date of note, May 24. Date of discount. May 24. 
 
 216. Face, $300. Time, 5 months Rate of discount, 6%. 
 Date of note, April 13. Date of discount, April 13. 
 
 217. Face, $420. Time, 2 months. Rate of discount, 8%. 
 Date of note, June 3. Date of discount, June 3. 
 
 218. Face, $1000. Time, 4 months. Rate of discount, 7%. 
 Date of note, July 24. Date of discount, August 3. 
 
 219. Face, $1200. Time, 3 months. Rate of discount, 5%. 
 Date of note, August 15. Date of discount, August 30. 
 
 220. Face, $2410. Time, 3 mouths. Rate of discount, 9%. 
 Date of 1 ote, Sept. 14. Date of discount, October 3. 
 
^s, is dis- 
 2.59. 
 
 » 
 
 lonths, is 
 
 from Sep- 
 7.28. 
 
 PARTIAL PAYMENTS. 
 
 153 
 
 m. Face, $390. Ti.ne 90 clays. Rate of discount, 10% 
 Date of note, October 14. Date of discount, Nov. 4. 
 
 222. Face, ^000. Time, GO days. Rate of discount, 12% 
 Date of note, July 3. Date of discount, August 1. 
 
 223. Face, moo. Ti„,e, 90 days. Rate of discount, 9%, 
 Date of note, June 3. Date of discount, August 13. 
 
 224. Face, $500. Tin.e, 45 days. Rate of discount, G% 
 Date of note, May 10. Date of discount. May 16. ' 
 ihis note bears interest at 7%. 
 
 225. Face, $2400. Time, 120 days. Rate of discount, 8% 
 Date of note, August 13. Date of discount, August 29. 
 ilus note bears interest at 5%. 
 
 226. Face, $385.62. Time m Hn.ra t> * r i- 
 
 , V .li-. mne, i.i.6 days. Rate of discount 10%. 
 
 Date of note, June 14. Date of discount, August 3. 
 J Ills note bears interest at 7^%. 
 
 he discount 
 
 It, 6%. 
 rch 13. 
 
 It, 6%. 
 24. 
 
 t, 6%. 
 113. 
 
 t, 8%. 
 3. 
 
 nt, 7%. 
 St 3. 
 
 int, 5%. 
 igust 30. 
 
 nt, 9%. 
 ber 3. 
 
 IV. PARTIAL PAYMENTS. 
 
 HINTS AND DEFINITIONS. 
 A partial payment is a payment of only a part of a debt 
 Of 2Z:r''^' '''"""* '' " "°*^ *« •"•«^° '* '^ *^^0"ed. - written on the.baek 
 An.'indorsement states the date and amount of the payment. 
 Special receipts are sometimes given for such payments 
 
 JoZZ'^ZZ" '"*""* "' ' "°*^' ^'"' ''-"^' P^-""-*« ^- ^een made, 
 
 1. Compute the interext to the time of the first payment. 
 
 2. Snltract the first payment /r.m the sum of the interest and principal. 
 
 3. Treat the remainder as a new principal. 
 
154 
 
 SIXTH DEPARTMENT. 
 
 BUSINESS EXERCISES. 
 Direction.— Compute intereat by the sixty-daj- method. 
 
 227. Note.- Date, June 15, 1886. Prin.,|?300. Time, 3 years. 
 Payments.— June 15, 1887, $120 ; June 15, 1888, $90. 
 How much is due at maturity (June 18, 1889) V Bate, 6%. 
 
 228. Note.—Date, Augusta, 1885. Prin.,$400. Time, 2 years. 
 Payments.— Nov. 3, 1885, $100 ; Feb. 3, 1880, $150. 
 How much is due at maturity ? Bate, 6%. 
 
 229. Note — Date, July 4, 1885. Prin.,$()00. Time, 90 days. 
 Payments — Aug. 15, 1885, $150 ; Sept. 3, 1885, $200. 
 How much is due at maturity ? Hate, 8%. 
 
 230. Note.— Date, May 3, 1886. Prin.,$450. Time, 3 months. 
 Payments.— June 14, 1886, $100 ; July 12, 1886, $210. 
 How much is due at maturity ? Rate, 4%. 
 
 231. Note —Date, Mar. 15, 1886. Prin. , $1000. Time, 120day9. 
 Payments.— April 16, 1886, $400; M,..) 3, 1886, $200. 
 How much is due at maturity ? Bate, 10%. 
 
 232. Note.— Date, Sept. 27, 1886. Prin., $1200. Time,8months. 
 Payments.— Oct. 14, 1886, $640 ; Jan. 3, 1886, $220. 
 How much is due at maturity? Bate, 6%. 
 
 233. Note.— Date, Nov. 27, 1886. Prin., $2540. Time, 60 days.. 
 Payments.— Dec. 13, 1886, $1140; Jan. 15, 1886, $360. 
 How much is due at maturity ? Batf, 6%. 
 
 234. Note.— Date, Mar. 15, 1886. Prin., $390. Time, 6 months. 
 Payments.— April 5, 1886, $120; June 21, 1886, $100. 
 How much is due at maturity ? Bate, 7 % . 
 
 235. Note — Date, March 3. 1885. Prin., $1000. Time, 3 years. 
 Payments— March 3, 1886, $100 ; Sept. 3, 1887, $300. 
 How much is due at maturity ? Bate, 12%. 
 
 236. Note.— Date, April 22, 1885. Prin., $1200. Time, 5mo8. 
 Payments.— May 3, 1885, $125 ; Aug. 7, 1885, $25. 
 How much is due at maturity ? Bate, 9%. 
 
REVIEW. 
 
 155 
 
 V. REVIEW. ■ 
 
 EXERCISES IN TRUE DISCOUNT. 
 
 NoTB.-The present worth of a debt due at some future time is Its value now 
 In busmesa. the present worth is the principal less the interest The ".presel; 
 
 and tH pHncipa. is ^ZS^l^^^^^Z ^r. ^^^Z^ 
 SebToTnftn "'■''' "'"^ "an*rf,-..,.„, i« the interest on thefac ofThI 
 debt. To find the true present rvortk, divide the face of the debt by the amount of 
 »1 for the given time at the given rate. If the interest = f of the principal, then 
 the true discount = ^--^ of the principal. The problems given below are of no 
 value whatever except as mathematical exercises. 
 
 atf%' ^'""^ *^^ ^'"^ '^'''''""*' "^ *" "^^^^ "^ '^^^^ ^"^ ^^ 3 y«^^« 
 
 239. Which is the better, to buy flour at $8 per barrel on 6 
 months credit or at $7.50 cash, money being worth 6%? 
 
 240. Find tlie difi"erence between the true and the bank dis^ 
 count of $307.50 due in 3 years at 7^%. 
 
 241. The interest of a certain sum is } of that sum. The 
 true discount is $12. What is the sum ? 
 
 242. Find the true discount of $4200, the interest for the 
 given time being $60. 
 
 243. The true discount of a certain sum is $70. What is the 
 
 ,„ «m' i^^*!"! *'"^ '^''"''""^ ^^' ^ y'^" '' ^^' ^"d the principal 
 IS $60, find the rate per cent. 
 
 246. If the true discount for 1 year is f of the interest, what 
 IS the rate per cent ? 
 
 J^^' 1^!. '"*^'^'* '''' ^ '""' ^^ '"°°^y ^^^ * ««^t^i« time is 
 $300, and the true discount is $240. Find the sum of moneya / 
 
 4 
 
 9m' 
 
 Mr^ 
 
 
 GK/v 
 
136 
 
 SIXTH DEPARTMENT. 
 
 / 
 
 247. The interest is ^ of the principal, and the difference be- h 
 twoen the interest and principal is «;120. Find the true present i Vl''^ 1 
 worth. * J ' 
 
 248. The interest is j^ of the principal. The difference be- -. 
 tween the n.terest and principal is $120. Find the true present vO^ ^ 
 worth. '■ \ 
 
 249. The sum of the interest, amount, true present worth, 
 and true discount of a certain principal is $1250. Find the ^ 
 amount. 
 
 MISCELLANEOUS DRILL EXERCISES. 
 DiBBCTiON.— Compute interest on a basis of 365 days, 
 
 260. In how many years will $1111. 10 double itself at 10% 
 8imi)le interest ? 
 
 261. The interest on a sum of money in 5 years is « of the 
 sum. What is the rate per cent ? 
 
 262. In 33.^ years the simple interest of a certain sum of monoy 
 IS double the true discount for the same time. What is the rate 
 of interest ? 
 
 263. I buy a horse, and sell him at a profit of $49, and find 
 tluit I make as much per cent as the horse cost me. How much 
 did the horse cost ? 
 
 264. What sum must be lent at 8% to produce a vrarlv 
 income of $4(550 ? $ A' Q / 3 ^^ ' ' 
 
 266. At what rate must $650 be lent to produce a yearly 
 income of $32.50? A^ 'V ^ ^ 
 
 266. The proceeds of a note of $350, which had 3 months to 
 run, discounted at a bank at 6%, were invest«d in wool at 35 
 cents a pound. How many pounds were bought ? 
 
 ^J^-oI\^J'^^ principal loaned for 48 days at 6% will amount to 
 ^o8t>.48? (Sixty-day method.) 
 
 \M ^^a^Ji^'"'^ """" "^'^ '"^ ^ y^^""' ^*^ ^^^ «™P^« i^t^^est amount 
 
REVIEW. 
 
 157 
 
 X 
 
 269. A and B invested f500 each for 3 years at 5 per cent- 
 A 8 at simple interest and B's at c.inpound interest. Find the 
 diiferenco in the amount of interest they respectively receive. 
 
 260. A grocer gives 11 pounds of sugar for U if cash is paid 
 and 10 pounds on one year's credit. What is his rate of 
 discount ? 
 
 261. An army lost 15% by disease, and 13% of the remainder 
 by battle. There are 29,580 men left. How many were there 
 at hrstl 
 
 262. If eggs are bought at 10 cents a dozen and sold at li 
 cents each, how much is gained per cent ? 
 
 263. If I buy at 60 cents a score, at how much a dozen must I 
 sell to gain 40%? 
 
 264. The interest on a certain sum for 9 months at 5% is |!150 
 less than the interest on the same sum for 15 months at 4% 
 Find the sum. 
 
 265. The amount of a certain sum at simple interest for 3 
 years is |558 ; for 4^ years it amounts to |G12. Find the rate 
 per cent and the sum. W u x^ * C Q 
 
 266. I borrow $540 at sii .pie interest for 5 years At the 
 end of each year the rate is raised 1 %. At the end of the time 
 the total interest is $189. What is the rate for the first year ? 
 
 267. How much water must be added to 80 gallons of wine 
 80% strong to make it 50% strong { 
 
 268. A sum of money has doubled itself in 10 years at simple 
 interest. What is the rate per cent ? 
 
 269. I desire to raise $994 50 by discounting 30-day notes at 
 
 Vl\ 11^"^ *^^ ^'''''^ ""^^"^ ""^ *^^ "«<^«»- (Sixty-day method. 
 Add 3 days grace). 
 
 270. A man failed to pay his tax when due December 1 1885 
 and was obliged to settle it April 1, 1836, with 2^% a month 
 and $2.50 costs added. He paid $29.45. Whaf, v.« \.\. +o^ i 
 
158 
 
 SIXTH DEPARTMENT. 
 
 -Y 
 
 ^. 
 
 271. For how many years must $126 be drawing intereht at 
 4% to amount to f200 ? U (J j/^ 
 
 272. Find Die simple interest of $840 for 2 years 7 months 
 24 days at 8 % . (Sixty-day method). 
 
 273. A retired merchant has an income of $25 a day his 
 property being invested at G % . What is he worth ? 
 
 274. Show tliat the difference between the interest and the 
 true discount of the same sum is the interest of the discount. 
 
 276. If the true present worth of $838 due in 19 months is 
 $800, what is tlie rate per cent ? 
 
 276. By lending a sum of money at 4%, and another sum at 
 5%, the totPl interest is $08. If the rates are interchanged the 
 interest is $67. Find the sum lent at each rate. 
 
 277. At what rate per cent will a principal double itself, at 
 simple interest, in 25 years ? 
 
 278. The interest of a certain sum is f of the principal The 
 amount is $G40. Find the principal. 'i V t D 
 
 279. At what rate per cent, simple inteiist, will a given sum 
 become four times itself in 20 years ? 
 
 280. A tradesman marks his goods with two prices, one for 
 ready money and the other for a credit of 6 months. What 
 fraction of the credit prices should the coot prices be, allowing 
 5 % simple interest ? 
 
 281. What yearly rate is equivalent to 8% compounded half- 
 yearly? What rate compounded quarterly is equivalent to a 
 yearly rate of 10lg%? 
 
 282. If a woman buys eggs at 9d. a dozen, how many ought 
 ahe to sell for 11 shillings to gain 10% ? 
 
 283. I allow my broker 1§%. How much do 1 owe him for 
 selling goods to the amount of £565 ? 
 
 284. In how many years will a man, paying interest at 7% on 
 a debt for land, pay the face of the debt in interest ? 
 
REVIEW. 
 
 159 
 
 288. A merchant sends $10,246.50 to l-is agent in Chicago to 
 invest m flour, after deducting his commission of 3^% of the sum 
 invested. How many barrels of flour can he buy at $5 50 ner 
 barrel ? ^ 
 
 286. A grocer buys sugar at 6 cents per pound. Allowing 
 12i% of his sales for bad debts, at what price must he sell it to 
 gain 16|%? 
 
 287. I bought an article and sold it so as to gain 10% If it 
 had cost 20% less and I had sold it for «1 less I would have 
 gained 26 % . Find the cost price of the article 
 
 MISCELLANEOUS BUSINESS EXERCISES. 
 
 DrRBCTioN.-Cor.pute interest and discount by the sixty-day method. 
 
 Transaction.— Toronto, August 3, 1886. F. M. Knowler 
 gives T. (iibson an order on C. Fraser & Co. for $25, to be paid 
 in goods from his store. 
 
 288. Write the order. 
 
 289. Gibson gives Knowles a receipt. Write it. 
 
 Transaction.-New York, July 5th, 1885. S. S. Packard 
 borrows $450 from D. T. Ames, and gives his note at ninety days 
 m payment. '' 
 
 290. Write this note. Make it payable to bearer. 
 
 291. When will it be due ? 
 
 292. If interest were charged ai 6%, how much would be due 
 at maturity '\ 
 
 Transaotion.-New York, July 12, 1085. D. T. Ames has 
 Packard's note discounted at the First National Bank at 7%, 
 and receive-^ cash in return. 
 
 293. Indorse the note before discounting it. 
 
 294. How much cash should Ames receive ? 
 
160 
 
 SIXTH DEPARTMENT. 
 
 !i 
 II 
 
 Transaction.— Chicagu, September 4, 188(5. Richard Leea 
 buys go(xl8 U) the amount of $35.80 from D. E. Lantz .i Co., and 
 gives his check on tlie Second National Bank in payment. 
 
 295. Write this check. Miike it payable to f)rder. 
 
 296. Indorse the check, making it payable to J. Tait's order. 
 
 Transaction.—St. Louis, November 15, 188(5. W. A. Beer 
 borrows $337 from E. P. Rowell, and gives his note at three 
 months in payment. Interest 7 '/c . 
 
 297. Write this note. Make it ;)ayablo to order. 
 
 298. When will it be due ? 
 
 299. What amount will bo due at maturity ? 
 
 Tran8accion.-St. Louis, Decembers, 188<i. E. P. Rowell 
 has Beer's note discounted at the First National Bank at Sfc and 
 receives cash in return. 
 
 300. Indorse the note before discounting it. • 
 
 301. How much cash should Rowell receive ? 
 
 Transaction. -Baltimore, March 3, 188(5. S. E. Grover 
 buys of S. G. Pryor 320 barrels of flour at $5.20, and gives in 
 payment cash $1000 ; balance on account. 
 
 302. Make out S. E. Greer's bill. Receipt it. 
 
 Transaction.— Baltimore, April 3, 188(5. S. G. Pryor draws 
 a draft at 30 days sight on S. E. Grover, Portland, for tlie 
 balance of las account. The draft is in favor of E. J. Garrison 
 Troy. 
 
 303. Write the draft. 
 
 304. Accept it for S. E. Grover. Date, April 5 
 
 Transaction.- Troy, April 8, 188(5. E. J. Garrison has the 
 draft discounted in the Trader's Bank at 10% and receives cash 
 in return. 
 
 305. Indorse the draft for E. J, Garrison. 
 
 306. How much cash should he receive i 
 
SEVENTH DEPARTxMENT. 
 
 I. STOCKS AND BONDS. 
 
 HINTS AND DEFINITrONS. 
 rae c.pi W Mock Of . company „ divided l„to *.„. u.u.llj „, „«, .„ch 
 
 The market value of . ,h.r<, ., the ,„,„ ,„, „h,ch'i, „,. ^ „„ 
 
 ont"rof::ior''''''*''-^*''''''°'''''"'«'''-*-"'''">»'epo,oo„. 
 
 M tho Intosl becomes due °" """'«' '""" «"» »» «■"» 
 
 Console are Engll.h Ooven.menl securitie. 
 
 self against loss. ^ "'^ *'*°^"'* *'"' Protect him- 
 
 BUSINESS EXERCISES. 
 
 1. How much stock will $7200 buy at 80? 
 
 2. How much stock will |1G,800 buy at 75 ? 
 
 3. How much stock will $23,750 buy at U8| ? 
 
162 
 
 SEVENTH DEPARTMENT. 
 
 — |i ir 
 
 4. How many shares will $2767.50 buy at 92| ? 
 
 6. What is' the market value of 210 shares at 95 ? ^ . 
 
 6. What is the market value of 322 shares at 88| ? 
 
 7. What is the market value of $4200 stock at 78| ? 
 
 8. The par value of stock is $6000. Find a 4% dividend. 
 
 9. The par value of stock is $7200. Find a 3|% dividend. 
 
 10. The par value of stock is $9600. Find a 6% dividend. 
 
 11. What is the market value of $7200 stock at a premium of 
 
 7i%? 
 
 12. What amount of stock must be sold at 82.^ to produce 
 $3300 ? 
 
 13. If stock is quoted at 92|^, what is the market value of 150 
 shares ? '' 
 
 14. What is the market value of $14,400 stock at a discount 
 of 6^%? 
 
 15. What per cent is realized by investing in stock at 120 
 paying 6% dividend? 
 
 16. What sum must b*) invested at 90 to produce an income of 
 :$720 if the rate of divide, u is 8 % ? 
 
 17. Whc^t income is derived from investing $0545 in stock at 
 93^ paying a quarterly dividend of 2 % ? 
 
 18. How many shares of New York Central Railway stock can 
 be bought for $4125 at 82^, brokerage J%'? 
 
 19. What income is derived from investing $2345 in stock at 
 117|^, paying a semi-annual dividend of 3|% ? 
 
 20. At what rate should stock paynig annual dividends of 
 12 % be bought to realize 7| fo on the investment ? 
 
 21. How many shares of railroad stock at 15f % premium can 
 be bought with $8111.25, allowing |% for brokerage ? 
 
 22. A. quarterly dividend of 2^% was declared by a man"fac- 
 turing company. What was the income from 221 shares ? 
 
STOCKS AND BONDS. 
 
 163 
 
 and sold the same at 1§ % premium. Find his net profit ? 
 
 at m' 1\'^^T"^'' '^^'^'^'"^ "^ ^^^^ ^« ^^'^^^^^d «^ «t«ck bought 
 at 84, what ,s the rate of annual inconie on the investment ? 
 
 at l!'/diT'" 'f ' '^''"f . ' ^'"^''' ^'* «^^^«« '^^ ^'^"ro-.ul stock 
 at 2J% discount, paying ^ % brokerage. What did he receive ? 
 
 26. A bank with a capital of $500,000 declares a dividend of 
 7/0. How much will a stockholder receive who owns 27 shares ? 
 
 27. A railway company whose capital stock is $3,225 000 de- 
 clares a dividend of 4^%. WLat is the amount of the di;idend ? 
 
 Jl t ?P;^^»lator sold, through a broker, 96 shares of telegraph 
 
 Ju/l ^^^' T"T! """'* ''"'^ P"^^"^ " half-yearly dividend 
 of H/c be purchased to enable the buyer to realize 10% on his 
 investment? ^/o un ma 
 
 30. Which is the better investment: stock paying a regular 
 annual dividend of 6% and bought at 90, or stock paying 8% 
 dividends and bought at 120 1 f^y^'^S o/o 
 
 Jh ^;P^«"J^*"r paid $17,920 for 224 shares of stock, and re- 
 alized 5% on his investment when the annual dividends were 
 paid. What was the rate per cent of dividend ? 
 
 32. How much should I pay for 40 shares of railway stock at 
 3^ fo discount, the broker's charge being ^ % ? ^ 
 
 «.lf * "^.^f^,*^^"^^" ^^«^^«« to invest in U S. bonds at Ufc 
 
 $1620 for his invalid son. How much should he invest ? 
 
 34. If I buy a 6 % town bond at 112, .-^.c is my rate of income ? 
 
 36. What premium may I pay for Ninth National Bank stock 
 which declares a dividend of 10% so as to realize 7^% on my in- 
 vestment ? • 2 / "" "ly m 
 
 f -maits p I 
 
164 
 
 SEVENTH DEPARTMENT. 
 
 II. EXCHANGE. v 
 
 HINTS AND DEFINITIONS. 
 
 The system by which merchanta in distant places discharge their debts to each 
 other without the transmission of money is called exchange. 
 
 The business of exchange is usually conducted through the medium of banks. 
 
 A draft, or bill of exchange, is an order written by one person or bank direct- 
 ing a second person or bank to pay a specified sum to a third person. 
 
 Bills of exchange are negotiable or non-negotiable upon the same conditionSy 
 and are subject to the same indorsements, as notes. 
 
 The face or par of a bill of exchange is the sum expressed therein. It is the 
 original obligation exclusive of interest, premium, discount, etc. 
 
 " When Chicago owes New York the same amount that New York owes Chicago, 
 exchange will be at par ; that is, drafts will sell at their face value. When Chicafso 
 owes New York more than New York owes Chicago, drafts on New York will sell at 
 a premium ; there will be more buyers of exchange than sellers, and drafts will 
 sell for more than their face value. When Chicago owes New York less than New 
 York owes Chicago, the demand in Chicago for draft-i on New York will be les^s than 
 the supply, and drafts will boll for less than their face value, or at a 'Uscount," 
 
 Exchange on England is usually quoted by giving the value ot £lin dollars and 
 cents. 
 
 The intrinsic par value of £1 is $4.8665. 
 
 BUSINESS EXERCISES. 
 
 36. How much exchange on London at 4.81| will $821.99 buy? 
 
 37. Find the cost of a bill of exchange on London for £320 
 
 at 4.81|. 
 
 38. Find the coat of a bill of exchange on Liverpool for £420 
 lOs. at 4.87i. 
 
 39. Find the cost in St. Louis of a draft on St. Paul for $4700 
 at J % discount. 
 
 40. Find the cost in New Orleans of a draft on Chicago for 
 $9600 at J% premium. 
 
 41. What is the value in Mobile of a draft on New York for 
 $4000 at § % premium ? 
 
 42. The cost of a $720 draf* on Rochester wa»$722.70. What 
 was the rate of exchange ? 
 
EXCHANGE. 
 
 165 
 
 43 What is the value of a 30-day draft on Beaton for S4200 
 at i % discount and interest at 6 % ? ^ 
 
 S8M0 J^t*!,' *^' "^^^"^ ^^ ^ ^^■^••^y ^''^^^ «" Philadelphia for 
 ^000 at §% discount and interest 6%. 1 ^^^ lor 
 
 ihfn' 7^t T *^' P'"'"""^' ^^ ^ ^^^^<^ °f £840 10s. 6d sold 
 through a broker at 4. 82f , brokerage ^ % ? 
 
 distil'' wT f- "t'' !' ^''''' '"^"^ '^^ ^^*« «^ -<^hange f % 
 aiscouui. What IS the value of the draft? 
 
 for^L^at IV"' "'" "' I ''-'^^ ^'^ ^^y«> ^^-^* - Chicago 
 lor ^UJO at i % premium and interest 6 % ? 
 
 NoTB.-Subtract the interest and add the exchange. 
 
 48. How large a 90-day draft must I draw so that when sold 
 at will produce |1000; exchange ^%, discount and interest W 
 
 ^foO t ^r/" ^^"f "'*^ ^""^^' " '^■^'^y ^^'^f^ «- Boston for 
 oTthet'fu'^""'"^*^ ''''-' '''''''''''- ^^^-^-- ^^-ost 
 
 of tot ar24t:i:tsTpt^^^^^ ^-rr^^ -"« ^^'^^« p-^^« 
 
 ^. 1, 1* pound. If lus commission is 4% and 
 
 ^.change i% premium, how large a draft can I« buy to se ,d to 
 the consignor in Toronto ? 
 
 61. What is the cost of a draft on New York for iftfinn ,^. 
 course of exchange being 100| ? ^^^' *^" 
 
 v.^^'^y^'lM^''' ^""'^ ""^ ^ ^'""^^ «^ ^«^ York that can be pur- 
 chased for |1234.37i the course of exchange being 98| ? 
 
 ^efo" /rT.""'!'!"" ^'''''^'""* '"^^ " consignment of peacliesfor 
 ^640^ and a ter taking out his commission of 5% bought a draft 
 on Wilmington at |% discount. What was the face of the draft ? 
 64. A sight draft on Pittsburg was bought for $1771, exchange 
 being at a premium of f %. Find the face of th! draft 
 
 ml5 ?^^''* "''''* ^' "'' ^''' "^ " ^'"^' ^' ^^^^ ^^«««""^ *« ^'ost 
 
 ..^; „^^i ^' '^' "'^^"^ f ^ ^ ^^-^^y draft on San Francisco for 
 
 T'-«".v a-, g ;-c premium and interest at 7 % ? 
 
! 
 
 166 
 
 SEVENTH DEPARTMENT. 
 
 III. INSURANCE. 
 
 HINTS AND DEFINITIONS. 
 
 Insurance is indemnity secured against possible loss or damage. 
 
 The policy is the contract or agreement between the insurer and insured. 
 
 The premium is the sum paid for insurance, and is usually a certain percentage 
 of the amount insured. 
 
 The premium ratCS depend upon the nature of the risk and the lenj; s of time 
 for which the policy is issued. 
 
 Fire insurance companies do not usually insure propertj' for its full value. 
 
 BUSINESS EXERCISES. 
 
 57. What will it cost to insure a house for $3600 at 2^%? 
 
 58. What will it cost to insure a barn for $500 for 5 years 
 at3%? 
 
 59. Find the cost of insuring a cargo of goods for $12,000 
 
 at^%. 
 
 60. What will it cost to insure a mill worth $18,000 for | of 
 its value at 1|%? 
 
 61. A company charges $60.75 for insuring a house for $2700, 
 What was the rate of insurance ? 
 
 62. I- paid $1443.75 for insuring 5000 barrels of flour worth 
 $5.25 a barrel. What was the rate of insurance ? 
 
 63. What is the premium for insuring a cargo of 4840 bushels 
 of wheat, valued at $1.20 a bushel, at 1J% on f of its value ? 
 
 64. A man paid $350 for insuring his dwelling at §% for one 
 year. If destroyed by fire how much is he entitled to receive ? 
 
 65. A building was insured for $3000 in one company at 1^%, 
 and for $4000 in another company at 1| % . What was the total 
 premium paid ? 
 
 6G. A company insured a business block for $90,000 at ^%. 
 At the end of 5 years the block was destroyed by fire. If | of 
 the claim was paid how much did the company lose ? (Interest 
 not considered.) 
 
BANKRUPTCY. 
 
 167 
 
 IV. BANKRUPTCY. 
 
 HINTS AND DEFINmONS. 
 
 A liability is a debt owing by a concern. 
 
 The net worth of a concern is the excess of its resources over its liabilities 
 resource?* Insolvency of a concern is the excess of its outside liabilities over its 
 
 If a concern is unable to pay its debts it is said to be bankrupt, or Insolvent 
 The assets of a bankrupt include debts due to him by others. 
 The creditors are the persons to whom the bankrupt is indebted. 
 
 BUSINESS EXERCISES. 
 
 67. A man's assets are $3000 and his liabilities $4000 How 
 much can he pay on the dollar ? 
 
 68. A man's resources are $4800 and his liabilities $7200 
 flow much can he pay on the dollar ? 
 
 69 A bankrupt pays 37J cents on the dollar. How much 
 ^:il be lost by a creditor whose bill is $750 ? 
 
 70. A bankrupt pays 42 cents on the dollar. How much will 
 be lost by a creditor whose bill is $378 ? 
 
 71. A merchant bought a bankrupt stock at 45 cents on the 
 dollar and sold it 10 % below the original price. How much per 
 cent did he gain ? ^ 
 
 72. How much should a bankrupt pay on the dollar if his lia- 
 bilities are $15,000 and his assets $4000 ? 
 
 73. A jobber bought a bankrupt stock at 3U cents on the 
 dollar and retailed it at 10% above the original wholesale price 
 His expenses were 5 % of the total sum of money received. Find 
 his gain per cent on the goods. 
 
 74. A bankrupt's liabilities are three times as great as his 
 ^sets. A certain creditor sold his goods at 25% above cost. 
 
 "hat per cent docs he lose ? 
 

 168 
 
 SEVENTH DEPARTMENT. 
 
 f' 
 
 F 
 
 V. PARTNERSHIP. ^ 
 
 HINTS AND DEFINITIONS. 
 
 I 
 
 A partnership is an associition of two or more persons for the purpose of con- 
 -Jucting business. 
 
 Such an association is called a firm, a hcuge, or a company. 
 Each individual of the association is called a partner. 
 An active partner is one who is publicly known as such. 
 A silent partner is one who, though actually a partner, is not publicly known. 
 A special partner is one who furnishes a certain portion of the capital of the 
 firm, and holds him.self liable for that amount only. 
 
 A nominal partner is one who has no real interest in the business, but who 
 assumes the responsibility of a i)artner by lending his name and credit. 
 
 The investment of a firm is the aggregate of tlie money or property jointly 
 contributed by the partners. 
 
 Tlie net gain is tl>e excess of the total gains of a firm over its total losses 
 within a certain period. 
 
 BUSINESS EXERCISES. 
 
 75. A and B form a partnership to carry on a dry goods busi- 
 ness. A invests $2000 and B invests $5000. Divide a gain of 
 $20(55 in proportion to the investments. 
 
 76. A, B, and C gain $6335 in a speculation. A invested 
 $2400, B S3200, and C $1400. How much of the gain should 
 each partner receive ? 
 
 77. X, Y, and Z rent a pasture for 5 months at $16.20 a 
 month. X puts in 3 horses for 3 months, Y puts in 6 horses for 
 2 months, and Z puts in 7 horses for 5 months. How much of 
 the rent should each pay ? 
 
 78. A starts in business at the beginning of the year with a 
 capital of $3600. At the end of 6 months he takes in B as a 
 partner with M20Q capital. They gain $3420 during the year. 
 How much of the g in should B receive ? 
 
 79. A and B agreed to do a piece of work for $130. A worked 
 7 days of 6 hours each, and B worked 5 days of 6 liours each. 
 How much should each be paid ? 
 
PARTNERSHIP. 
 
 169 
 
 S2m '^;?;"^P^"*^^« '-^^ - -"tract of hu^^^^r^^V^^^^, 
 ■mbl The one works steadily for 32 days of 10 hours each • 
 the other works 24 days of 8 hours each. They pay ZlTt 
 matenal. How much of the profit should each receive ? 
 81 Two teachers, A and B, establish a private school Thev 
 
 Zlmr'L't' '-'''' ^^"^"^- ^-^"« the year A rec^v:^ 
 cash^520, and pays expenses m cash $127 ; B receives cash $470 
 and pays expenses m cash $92. How much n.oney should A pay 
 B to make an equal division of the gain ? ^^ 
 
 ^9^ ■ '^^" '""^' ^ ^'^d N' are associated in trade. M receives 
 
 n ^ITs th r %^ f "^^^ '"^ '"^^"^^''"^ t^- businesl Th 
 net gam IS then divided equally. Their sales for a certain vear 
 
 amount to $9320, and their books show a gain of $4^20 befo" 
 M s special interest is paid. Find N's share of the net gain 
 
 83. Drs. P and Q are associated in professional work" Thev 
 each receive and pay cash. On January 1, 1885, their bank 
 
 cash $3420, paid oftce expenses $142, and deposited $1340 
 During the same time Dr. Q received cash MfLl , i ^ 
 expense, |94. and aepo.tea''«B,^X',!^,% r ,"*- 
 
 ^ztn:-r '" '"^"- ^''-' "-^ ^"- "^'-^ 
 
 84. A, B, and C are partners. A puts int.) the conoen, Imm 
 bu withdraws half o, it at the end of 6 „,„„ths ; Bputs " S 
 and adds *10fl« to it at the end of 4 n.onths ; V .JlT^,; 
 
 t::!::xiZe^^'' '"" '"^'"^ "-^ ^-^ '- '^^»«- ^^..at is 
 
 Thfi ■^''^o" ;™'™<='°" agree to build a bridge for $14,188 
 
 It fr r. r" "' "'""■'' ''"• '' "»^» -'• 2» "«n for 32 days' 
 I T^ o. "" ^^ """" '"■■ ^^ ■^^y ""d 80 ,„en for 35 days The 
 thrd has 24 men for 50 days. The first receives $250 for superin! 
 tending the work. How m„ch is each contractor entitled to" 
 86. A and B lure a car for $84 for the purpose of shipping 
 
 te *°--": JW agree that the costof a horse and an ox shall 
 
 Divide the cost. 
 
170 
 
 SEVENTH DEPARTMENT. 
 
 VI. SQUARE ROOT. '^ 
 
 HINTS AND DEFINITIONS. 
 
 When a number is inultiplierl by itself the result is called the square of the- 
 number. 
 
 The square root of a given number multiplied by itself will pro<luce the giver* 
 number. 
 
 The square root is usually indicated by the sign »/. 
 
 The square root of a small number can be found either by Inspection or by 
 factoring. 
 
 Illustrative Exercise. 
 Find the square root of 7056. 
 
 The prime factors of 7056 are 2, 2, 2, 2, 3, 3, 7, and 7. 
 These can be divided into two groups of 2, 2, 3, and 7 each. 
 Then 2 x 2 x 3 x 7 = 84 = the square root of 7056. 
 
 WRITTEN DRILL EXERCISES. 
 Direction.— Find the square root. 
 
 87. 196. 
 
 88. 225. 
 
 89. 529. 
 
 90. 361. 
 
 91. 729. 
 
 92. 1024. 
 
 93. 5625. 
 
 94. 4096. 
 
 95. 5184. 
 
 96. 6561. 
 
 97. 17956. 
 
 98. 11664. 
 
 99. 17424. 
 
 100. 21025. 
 
 101. 10384. 
 
 102. How long must the side of a square lot be to contain 2^ 
 acres ? 
 
 103. One-half the square of a number is equal to 20808.. 
 Find thret; times the number. 
 
 104. A square lawn contains 576 square yards. What is the; 
 length of one side ? 
 
 105. A garden contains 1875 square yards, and it is three times 
 as long as it is broad. Find its length and breadth. 
 
 106. The product of the sum of two numbers by their dif- 
 ference is 756. The smaller number is 12. Find the larger. 
 
REVIEW. 
 
 171 
 
 ii 
 
 VII. REVIEW. 
 
 MISCELLANEOUS DRILL EXERCISES. 
 
 107. My inco: a tax at 18 mills on the dollar is $10.80. On 
 what amount do I pay tax ? 
 
 x.^r!.??'r^'"'^ ,'''''' difference made in income by the transfer of 
 £7080 from the 3 per cents at 05 to the 3^ per cents at 00. 
 
 109. If U men can do in 12 days as much as 21 men and 4 
 boys can do m 7 days, how many boys are equivalent to 9 men ? 
 
 110. A jeweler made three $2 rings from 85 worth of gold ,«„ 
 fine How many U rings would he make from $0 worth of pure 
 gold ? ^ 
 
 111. A horse thief going at the rate of 8 miles an hour has 32 
 miles of a start. He is pursued at the rate of 10 miles an hour 
 In how many hours will he be overtaken ? 
 
 112. I sent my broker $1248 to invest in flour at $4 a barrel 
 How many barrels can he purchase after deducting his commis- 
 sion of 4 % on the sum invested ? 
 
 113. A house is insured for | of its value at 1A% The 
 premium is $405. What is the value of the house ? " 
 
 114. If 6 iron bars 4 feet long, 3 inches broad, and 2 inches 
 thick weigh 144 pounds, he ^ much will 15 weigh, each 6* feet 
 long, 4 inches broad, and 3 inclies thick ? 
 
 115. A man has an income equal to 10% of his capital He 
 pays a tax of $164, which is 2^ per cent of his income. What 
 IS his capital ? 
 
 116. A gold ring is 18 carats fine. Find the percentage of 
 alloy in it. ^ 
 
 ,}}'^' t "^^ ''''''^^'''^ ^^'^^^ inhabitants. It has increased 
 10 /. in 10 years. What was its population 10 years ago ? 
 
 118. The true discount is ^ of the interest of the same sum 
 ant.t at the sanic rate. Find the rate. 
 
172 
 
 SEVENTH DEPARTMENT. 
 
 119. The interest of a certain sum is $36. The true dis^o • 
 ^2. Find the sum. 
 
 120. The bank diacount exceeds the true discount on 
 tain sum for 4 years by $11 )j, and for 8 years by $40. Ffua 
 sum and rate. 
 
 121. What sum must I in\ est in 5 % stock at 105 so thr r 
 paying an income tax of 8 cents in the dollar I may have a 
 yearly income of $1840 ? 
 
 122. A fails in business owing $7200. His assets are $3000. 
 How much will B receive if A owes him $450. 
 
 123. Allowing the net sum to be raised by a corporation to be 
 $9700, and the allowance for collection to be 3%, what is the 
 gross amount to be assessed ? 
 
 124. The premium for insuring a school-house at 2 % was $40. 
 For what sum was it insured ? 
 
 126. A premium of $64.80 was paid for the insurance of $8640 
 on stock of goods. What is the rate per cent of insurance ? 
 
 126. My house is valued at $2500 ; furniture, $1000 ; library, 
 $1000. I insure the whole for f of their value at f % . What is 
 my annual premium ? 
 
 127. A grocer gives 14 ounces for a pound. How much does 
 he cheat a cuf ' jmer who trades with him to the amount of $40 ? 
 
 128. What is the value of my property if I pay $648. 12^ taxes 
 at 15^ mills on the dollar, and am assessed at f of the real value ? 
 
 129. A contractor agreed to build a house in 60 days, and 
 employed 16 men. If his time is extended 15 days how many 
 men may he discharge ? 
 
 130. A merchant insures goods at 2 % for a sum sufficient to 
 cover both the value of the goods and the premium. The goods 
 are destroyed by fire and 75 % of the claim is paid. The mer- 
 chant gets $782 less than the value of the goods. Find this 
 value. 
 
REVIEW. 
 
 173 
 
 «PI 1 74. 20 when excliange m quoted at 4.89^ ? 
 
 133. What nrincipal will gain as much inteiest at 5% a« Jl2r,0. 
 will gain at 6 % in the same time ? ^^lo:^^ ^J50 
 
 134. A has 50% mere money than li. B's money is what vev 
 cent less than A's ? ^ P®" 
 
 136. Ten per cent of ? of a thing is what p«r ce»t of f of it ? 
 
 SllGts"^ m'^f "'*lT " ^^''""^^'"^^ «f 2if. an agent reraitrodl 
 »140.J6. What was the amount collected ? 
 
 137. What must I ask for an article which cost me ^0 so that 
 I can allow a discount of 33 J % and still make 20 % ? 
 
 138. A sewing machine was sold at a net profit of 40% on the 
 
 lis «C wr f"'t '\''^ ^^'^"« P"^« ^* ''^^- I^ "- cost 
 .vas 185100 what was the asking price ? 
 
 /JJ. 1* md his gain per cent. 
 
 sam^it f/'r' ^^ 'f"'i'^ ^'^'P^''"' ^*^^^ *^^ 10^ «"^ «old the. 
 sam. At 2% discount. How much did I lose ? 
 
 oo^^^' ^r^!,*^' '"*r!^ ""^ ^^^^-^^ ^^""^ ^^r^h 16 until October 
 28. (Sixty-day method.) ^-fooer 
 
 142. A certain sum in 6^ months at 8% amounts to $939 
 What sum would it amount to in 2 years? 
 
 stocf;tlo?^ '' '^' ^'"'' ^""^«*™^"*' 6^' «tock at 76 or 6%, 
 
 yearfat W ^^'^ ^"'''"''*' '''"'P''""^ ^"*^'^«^' «^ ^^00 for 2^ 
 
 146. A certain bank charges 9% discount. What rate of in 
 terest does it receive ? 
 
 146. How much must I invest in 4% stock at 84 to secure a. 
 net income of $1127 after paying an income tax of 2% ? 
 
174 
 
 SEVENTH DEPARTMENT. 
 
 147. The difference between the simple and compound interest 
 of a certain sum for 3 years at 6% is $55.08. Find the sum. v 
 
 148. If the interest equals ^\ ff the principal, what fraction 
 of the principal is the true discount ? 
 
 149. I bought 7200 bushels of wlieat at 87i cents on a credit 
 of 6 months, and immediately sold it for 88 cants cash. I lent 
 the money received for the full time at G % . Find my gain. 
 
 150. A bought goods to the value of $1400 and sold them to 
 B at a certain gain per cent. B sold them to C for $1694 at the 
 same rate of gain. What did B pay for the goods ? 
 
 161. Goods marked 45% in advance of cost are sold at a dis- 
 count of 20% on the marled price. What did a lot of goods cost 
 if the gain on them was $25.20 ? 
 
 152. A's income in 1884 was 50% greater than B's. In 1885 
 A's increased 10% and B's decreased 10%. Together in 1885 
 their incomes amount to $7650. Find the income of each in 
 1884. 
 
 153. An agent's commission on sales at 1§% was $88. Find 
 his employer's net receipts. 
 
 154. If a mere' ant adds 30% to the cost price of goods to make 
 his selling p..„e, what per cent must he deduct from his selling 
 price to reduce it to cost price ? 
 
 155. In a mixture of water and wine the water is 15% of the 
 wine, and when 15 gallons of water are added the water is 22|% 
 of the A^ine. Find the original quantities. 
 
 156. A merchant sold a portion of his stock for .^ISOO. This 
 was 15 % of the value of what remained. Find the value of the 
 original stock. 
 
 157. The entire profits of a business for 2 years amounted to 
 $7560. For tlie second year tlie profits were 10% greater than 
 the profits of the first year. Find the profits for each year. 
 
 158. A factor sells 800 barrels of flour at $6.52^- and remits 
 the net proceeds, $c089.50. Find his rate of commission. 
 
REVIEW. 
 
 17^ 
 
 159. If a boat is rowed at tlie rate of 6 miles an hour and is 
 driven 44 feet in 9 strokes of the oar, how many strokes are 
 made m a minute ? j o uie 
 
 ).,• ^^0- i;^g^°«\^««"« 7 pounds of butter for what 8 pounds cost 
 mm. What is his gain per cent ? 
 
 161. A bookseil-^v buys books at 25% and 10% off list ndces 
 and sells at list prices. What per cent profit does he make ? 
 
 bul^^i?"'" "^f'J^'^'^y «l^o"ld I send my agent that he may 
 buy 3000 pounds of tea at 36 cents and retain his commission of 
 4% of the sum invested ? 
 
 163. A buys an article and sells it so as to gain 12A% If he 
 had bought it at 10% less and sold it for $18 less he would have 
 gained $20. Find the cost of thu article. 
 
 164 A farm is rented for $300 in money and a certain number 
 
 i mtt r'- T"" "-"''^' ^^ '' ^^"*« ^ ^-^-1 the rent 
 18 12i% lower than when wheat is $1.20 a bushel. Find the 
 number of bushels of wheat. 
 
 165. A merchant bought a quantity of cloth and marked it at 
 an advance of 40%. In selling he used a yard-stick 1 Lh 
 short. His total gain was $330. Find the cost price of the cloth. 
 
 166. A sum of money in 10 years at 5% simple interest 
 amcnmts to $1250. In how many years more will it' amours 
 
 167. The interest of $200 equals the true discount on $240 
 money being worth 6 % . Find the time for which the latter sum 
 18 discounted. 
 
 168. A farmer buys a farm for $8000 and pays casli $3000, the 
 balance of the price remaining on r mortgage at 6% If the 
 nicome from the farm is $450, what rate of interest does he 
 obtain for his money ? 
 
 169. If the property of a city is valued at $21,000,000 and a 
 man who owns property assessed at $7000 pays $120 taxes' what 
 is the iiotal tax levied ? 
 
176 
 
 SEVENTH DEPARTMENT. 
 
 I 
 
 MISCELLANEOUS BUSINESS EXERCISES. ^ 
 
 Direction.— Compute interest and discount by the sixty-day method. 
 
 Transaction.— St. Louis, May 4, 1886. W. H. Sadler givoa 
 J. P. Lindsay an order on W. H. York & Co. for $37.50, to be 
 paid in goods from his store. 
 
 170. Write the order. 
 
 171. Write W. H. York & Go's account r'-ainstW. H. Sadler. 
 
 Transaction.— Chicago, June 13, 1886. F. Wood buys of 
 Aclor & Merrall, on 30 days' credit, 10 hhds. Sugar, 15,500 lbs., 
 at 9^c., and 20 chests Young Hyson Tea, 1250 lbs., at 53c. 
 x\ugust 1, F. Wood gives a check on the Sixth National Bank 
 in payment. 
 
 172. Write Acker & Merrall's invoice. 
 
 173. Write a statement, July 31. 
 
 174. Write F. Wood's check. 
 
 Transaction.— Montreal, July 16, 1886. T. Wells borrows 
 $239 from H. Block and gives his • note at 00 days in payment. 
 Interest 10%. 
 
 175. Write this note. 
 
 176. What amount will be due at maturity ? 
 
 Transaction.— Montreal, July 25, 1886. H. Block has T. 
 Wells' note discoimted at the Bank of Montreal at 8 % and re- 
 ceives cash in payment. 
 
 177. Indorse the note for H. Block. 
 
 178. How much cash should H. Block receive ? 
 
 Transaction.— Burlington, August 5, 1885. T. Ha ■.:ri ",& 
 cash ^25.30 from his account in the Third Nat? mal Bank. Tiia 
 same day he deposits $422.85 and issues a che n. in favor of 
 E. A. Blakely for $14.90. 
 
 179. T. Hall had $193.84 on deposit. How mi<ch lias ho now ? 
 
 180. Write both checks. 
 
REVIEW. 
 
 177 
 
 Traasaction.-E. Trout, of Toronwrowes WrH. Brown of 
 
 Tronnn f . x> " ^'^'^' '^ '^^^^* ^'■^ft (date, May 15) on 
 
 m his (Brown's) own favor for the balance. ^ 
 
 181. Write both of these drafts. 
 
 182. Accept each for E. Trout. 
 
 183. Who will present tho ^20 /Ir.ff -^ t> -r^ 
 
 W. H. Brown's agent ? ' ^^ ^^ ''^^^^ ^^'*^^^' '^^ 
 
 184. Write W. H. Brown's letter to O. 1:. Powers 
 
 186. Write W. H. Brown's letter to E Trou^ notifv-" r ■ 
 that he is about to draw the drafts. ^ '^ '^'"^ 
 
 rowe?roo*f°''-~p''f '^^'^^'^' ^^y ^' 1^««- "^^ A. Cox bor- 
 rowed $220 from Richard Lees and gave his note at mA 
 
 drawing interest at 7%, in payment. At .aturi; a ^ym j^ 
 
 teiest at 8% was given to coves the balance. 
 186. Write both notes for Richard Lees 
 
 mafuLf "" ""' ""^ '^^'^ ^^ '^ P^^^ -^- «- —1 note 
 
 ^aate, May 3 for $75 in part pay-ent of an account of $265 He 
 asks permission to ciose up the account with a 90-day note • 
 
 188. Writ€ the letter for J. . . Sparling. 
 
 189. Write tlie ()0-day note. 
 
 190. When wi> . it be due 
 
 191. Write W W.nia,™ & Co-s reply. (Favorable.) 
 m. Write W. WilUan., & Ws reply. (S„t favorable.) 
 
 193. I'' . ^rse the note for W Wilb'ana ^ n^ i • 
 
 able to the order o, J. 0. .TacLr "•' '"°'"'« " "^'^ 
 
 194. Fuul th-s interest on this note at 7%. 
 

 
 i 
 
 
 178 
 
 SEVENTH DEPARTMENT. 
 
 Transaction. -W. V. Wright, Hamilton, orders by telegraph 
 from Eldredge Bros., Philadelphia, 25 Hart's Composition (price 
 75 cents), and 50 Houston's Chemistry (price 
 
 195. Write the message for W. V. Wright. 
 
 196. Write the invoice for Eldredge Bros, (Discount 35%). 
 
 197. Write a letter acknowledging receipt of books. 
 
 Transaction.— Eldredge Bros, draw (date, August 3) on 
 W. V. Wright at 30 lays after date, their own favor, and have 
 the draft discounted at the Third National Bank at 8 % . 
 
 198. Write the draft. 
 
 199. Accept it for W. V. Wright. 
 
 200. Indorse it for Eldredge Bros. 
 
 201. What is the date of maturity ? 
 
 202. Find the cash proceeds. 
 
 Transaction.— Cassville, April 24, 1886. J. W. Elliott bor- 
 rowed "■ "^ from T. M. Henry and gave his note at 90 days, 
 -draw" ', ^rest at 8 % , in payment. At maturity tt payment of 
 $132 xde by Elliott and a new note at 2 months, drawing 
 
 interest ao 10%, was given to cover the balance. J. W. Elliott 
 paid the second note by a check on the First National Bank, at 
 which bank the note was jiayable. 
 
 203. Write the- first note for T. M. Henry. 
 
 204. Write the second note for T. M. Henry. 
 
 205. Henry requires an indorser. Indorse this second note 
 yourself. 
 
 206. When will the second note be due ? 
 
 207. Write the check. 
 
 I 
 
 ■• \^' 
 
EIGHTH DEPARTMENT. 
 
 r 
 
 EXAMINATION EXERCISES. 
 
 PAPER I. 
 
 2001V/ "^'^^^-''^ ^\-lf -l^at it is the quotient would be 
 ^UUl JUJ. What IS the quotient ? 
 
 2. I|nd the sum of the five largest numbers that can be ex- 
 pressed by the figures 2, 1, 0, 3, and 7. 
 
 IV^/h^i'ir'""'''^*'''' ''"'"''''' ^' ^^^' *^^^^ common factor is 
 1^ , th.. difi-erence between the other two factors is 2. AVI ■ are 
 the numbers? ™ 
 
 4. The sum of two numbers is 2472. Their difference is ^ of 
 the larger number. What are the numbers ? 
 
 6. Find the cost of 8540 pounds of hay at $22.50 a ton. 
 worfh a?eir^^' ^^ ^""^' '' '''' ^ ^^^^^ ^^ ^^^^ ^« ^^ 
 
 for £12^irs^*Od7'^''' '"^ ^'"''' '"^ ''"'" "' " ^- ^- "^""^y ^^••*^^' 
 
 8. A man earns $2.75 a day. How much will he earn Jn a 
 ynonth of July, the first da^ of whic]^ is Thursday ? 
 
 9. How many days from March 13, 1885, until July 14, 1887 ? 
 
 10. Copper weighs 560 pounds and tin 462 pounds to the 
 cub. foot. What will be the weight of a cubic foot of a mixtur 
 ot b parts copper to 5 parts tin ? 
 
Hi 
 
 i 
 
 11 
 
 1 
 
 ■■■■« 
 
 MMHM 
 
 
 180 
 
 EIGHTH DEPARTMENT. 
 
 PAPER II. 
 
 11. How many apples must bo out up to givo 300 boys ^ of an 
 api)lo each ? 
 
 12. Divide a sovereign between A, B, and C so tliat A may 
 have four i)ence tnore tlian H, and B ten pence more than C. 
 
 13. A and B togetlier have ^9000 ; 3 times A's money is to 4 
 times B's as 3 is to (>. How much has each ? 
 
 14. Find the cost of 2S>84 pounds of pork at )p7.85 })er humlred- 
 weiglit. 
 
 15. What will 4347 pounds of rice cost at 45 cents a stone l 
 
 16. How many inches are there in 2^ chains '/ 
 
 17. Two nuinberjS are to each other as 3A to 4jr. The greater 
 is 52 ; what is the less '! 
 
 18. How many sheets of paper are there in 2^ reams i . 
 
 19. Tf a ton of coal occupies 40 cubic feet, what will it cost to 
 lill a bin 12 feet long, (! feet wide, and 5 feet deep, with coal at 
 $<5.50a ton? 
 
 20. Two men or 5 boys can perform a piece of work in 7 days. 
 How nuiny men along with 3 boys would perform it in 3J days i 
 
 PAPER III. 
 
 21. Divide f()30 between two men so that their shares will be 
 to each other as 7 to 2. 
 
 22. The difference between J and ,\ of a nvuuber is 18. What 
 is the number i 
 
 23. Find the cost of building a fence around a piece of land 80 
 rods square at 20 cents a rod. 
 
 24. How much water is there in a mixture of 50 galloni of 
 wine and water worth $1 a gallon, if 50 gallo.s f)f wine cost ^60? 
 
 25. How much is received for 18 pails of berries, each con- 
 taining § of a peck, at 12^ cents a quart? 
 
KXAMINATfON KXKIKUSES. 
 
 ___^ 181 
 
 86. What will it cost to dig a collar 90 feet by 00 foot, ami 7* 
 foot (loop, at 'M) contH n cubic yard ? 
 
 27. Bought orangoH at 10 cont« a do/on and «ol.l thorn at 5 
 tor Jl couts. How much wan gaii.o.l on \[ l,oxo«, oach c.n- 
 tamuig 20 do/on ? 
 
 28. Thrco uu.n oaniod mtM) in duyn of iO b<,ur« oach 
 How much did oach rocoivo por hour? 
 
 29. I have an orchard 100 by 200 yur<l8. The trooH an. 20 foot 
 npart and 20 foot fron, tho fonoo. How nmny trooH arc thoro ( 
 
 ^?; ^ '"'''^"»;' "f ^•I'l'-'k •"»•' ««-tH.n toa weighing K} pounds is 
 worm 1117.50. If tho proportions of each aro intt.rciiangod tho 
 nuxturo will bo worth *8.J0. Tho black tea is w<.rth 70 cout« a 
 pound, h ind tho i)rice of tho groon toa. 
 
 PAPER IV. 
 
 31. How many hours woro thoro in tho yoar 1800 V 
 
 32. A (pmrtor-Hocti.m of land yielded -10 buHhol« of wheat to 
 tho acre. What waH roooive.l for tho crop at *2. 10 per cental ? 
 
 33. What will it coHt to bron/.o a cube, each odgo of which Ih 
 <i foot, at 1^ cents a mpiare inch '( 
 
 34. At fMS an acre a farm in worth $.'10(]0. Tt is HO i-ods wide 
 I^ind tho cost of fencing it ui 75 cents a rod. 
 
 35. How many coins, each half an inch in diameter, can bo 
 placed m rows, touching each other, on a table 3^ foot by (i 
 
 36. Find tho value of £15.()y5 in dollars and ce)its. 
 
 37. Find tho cost of 2i miles of barbed wire at \'i oonts a 
 yard. '' 
 
 38. The sum of two numbers is \)l and then- difTeronco is ^ 
 Four tm.os tho larger is how many times the nmallor '( 
 
 39. The owner of y^ t.f r mine sold jU^ of his share for 11(40,500 
 What should he who owns 'j uf tho mine got f<.r iJ <.f his share ? 
 
i 
 
 •m 
 
 182 
 
 EIGHTH DEPARTMENT. 
 
 40. If 20 men can perform a piece of work in 12 days, how- 
 many men can perform another piece of work three times a» 
 large in J of the time ? 
 
 PAPER V. 
 
 41. Find the sum of all the prime numbers between 125 and 
 IGO. 
 
 42. Tlio sum of two numbers is 100020002 ; their difference 
 is 90009001. Divide twice the larger by ^ 
 
 43. Find the value of a pile of wood 80 feet long, 20 feet 
 wide, and 14 feet high, at $3.20 a cord. 
 
 44. Wliat number is the same fraction of 7| that 3J is of 15 ? 
 
 45. How many inches in widtli must a lumber dealer measure 
 off in measuring 16-foot lumber, 1^ inches thick, to make 200O 
 feet? 
 
 46. How many boards 14 feet long and 10 inches wide will 
 be required to build a sidewalk 40 rods long and 4 feet 8 inches 
 wide ? 
 
 47. How many miles will a boy walk to plow 6 acres, turning 
 a furrow of 9 inches ? 
 
 48. How many apple trees, planted in rows 15 feet apart each 
 way, will be required to cover a plot of 7| acres, 40 rods long ? 
 
 49. A merchant sold 384 barrels of flour, part at $7.25 and 
 the rest at $5.50 a barrel. He received for the whole $42 more 
 than if he had sold all at $G.37| a barrel. How many barrels, 
 were sold at each price ? 
 
 50. How many tons of ice can be put into an ice house 20 feet 
 long, 12 feet wide, and 8 feet high, supposing ice to be ^^^ aa 
 heavy as water ? 
 
 PAPER VI. 
 
 51. What will it cost for sufficient inch lumber to build a 
 tight board fence 5 feet high around a 10-acre field, 80 rods; 
 long, if lumber costs $18 per M. ? 
 
EXAMINATION EXERCISES. 
 
 183 
 
 52. Find the cost of 3 gross of pencils at tlie rate of 3 f(,r 2 
 cents. 
 
 63. A horso trots 42^ nules in 8^ hours. At what rate per 
 hour does ho go? ^ 
 
 64. Bought 220 bushels of wheat at $1.30 a bushel and sold it 
 at I!|!l.o0 a cental. How much did I gain or lose ? 
 
 66. A house and lot cost $4200 ; the cost of the lot is § that 
 of the house. Find the cost of each. 
 
 «.?nA ^ JT''"''*" ^""^'^'^ •'' *''"^'''"' """'^*^'' "^ ^^^"•els o{ flour for 
 JI54400. He reserved 40 barrels for his own use and sold 4- of the 
 
 remainder for $3952, which was $608 more than cost. Find the 
 number of barrels he bought. 
 
 67. A regiment marching 4 miles an hour take 128 steps in a 
 mnuite. What is the length of each step ? 
 
 58 How many feet of lumber are there in a 2-inch plank 16 
 teet long and 9 inches wide ? 
 
 4 
 
 69. If a pint contains 28g cubic inches, how many pints of 
 water are there in a tank 11 feet by 7 feet, and 3 feet deep, 
 mled to the top ? ^ 
 
 60 The sum of two numbers is 35875, and their difference is 
 equal to 4 of the greater number. What are the numbers I 
 
 PAPER VII. 
 
 61. If a merchant sells | of an article for | of its cost, what 
 IS his gam per cent ? 
 
 62. A merchant buys cotton, and sells it at a profit of ^ of 
 the cost. Find the cost per yard if the selling price of 125 
 yards is equal to the profit on $30 outlay. 
 
 63. The product of two numbers is 28, and one of them is 
 o^ ; what is the other ? 
 
 64. If the unit in which something is expressed be increased 
 by one-third of itself, how must the number be altered ? 
 
m^ 
 
 184 
 
 EKiHTH DEPARTMENT. 
 
 
 X 
 
 66. How much will it cost to plaster a room 27 feet long, 16 
 feet wide, and 12 feet high, at 26 cents a square yard, allowing 
 432 scjuare feet for doors and windows ? 
 
 66. A man agreed to work for $1. 10 per day, and to forfeit 
 30 cents for each day ho was idle. At the end of 24 days his 
 wages amounted to $19.40. How many days did ho work ? 
 
 67. I have a rectangular farm, the perimeter of which is 240 
 rods. It is twice as long as it is wide. How many acres does it 
 contain ? 
 
 68. A vessel contains 3 parts brandy and 2 parts water. How 
 much of the mixture must be drawn off and replaced by water 
 that the new mixture may be half and half ? 
 
 69. What is the value of a rectangular held 60 rods long and 
 40 rods wide at $55 fin acre ? 
 
 / 70. A man rides a certain distance at the rate of 6 miles an 
 hour, and walks back the same distance at the rate of 3^ miles 
 an hour. If it takes him 4| hours to go both ways, what is the 
 distance ? 
 
 PAPER VIII. 
 
 71. What will be the expense of an oil cloth for a hall 6| 
 yards long and 12 feet wide at $1.35 a square yard ? 
 
 72. How many quarts of berries at 27 cents a quart will pay 
 for 14| yards of oirput at $1,875 ^ yard ? 
 
 73. A boy i)aid 20 cents for 200 apples and pears together, 
 buying 25 apples for a cent and 25 pears for 3 cents. How 
 many of each did he buy ? 
 
 74. How much water must be mixed with 80 gallons of wine 
 at $1.25 a gallon to reduce the value 75 cents a gallon ? 
 
 76. In a certain race A can beat B by 80 yards ; but the day 
 of the race proving foggy, A rows at f of his usual rate and B at 
 t"(j of his, when A beats B by only 26 yards. Find the length of 
 the course. 
 
 
EXAMINATION EXERCISES. 
 
 185 
 
 76. A yrmng man whose salary is $28 a week i^iys H7.50 a 
 week for board and $9.45 a week for other expenses. In how 
 many weeks can he save enough to pay a debt of ^.30.40 / 
 
 77. Find the cost of papering a room 36 feet h)ng, 24 feet 
 wide, 18 feet high, with paper 18 inclies wide at $1.50 a roll, 
 allowing 64 square yards for doors and windows. (One roll = 8 
 yards.) 
 
 78 A merchant's assets are !|4672 and his liabilities #5840. 
 How much can he pay on the dollar ? 
 
 79. How much copper must be mixed with 35 pounds of silver 
 of .9 fineness in order that the mixture may be of .7875 fineness ? 
 
 80. If 3 apples and 5 peaches can be bought for 37 cents, and 
 2 apples and 3 peaches can be bought for 23 cents, how many 
 apples can be bought for 20 cents ? 
 
 PAPER IX. 
 
 81. How many cubical blocks i of an ih, h on each edge can 
 be put into a cubical box 2 inches deep, 2 inches wide, and 2 
 inches long ? 
 
 82. A rectangular field 6^ times as long as it is wide contains 
 300 acres. What is the distance around the field ? 
 
 83. How high must wood be piled on a car which is 28 feet 
 long and 8 feet wide to contain 14 cords ? 
 
 84. I have (ii hours at my disposal. How far may I drive at 
 8 miles an hour that by walking back at 31 miles an hour I may 
 have 22^ minutes to rest ? 
 
 85 Two cogged wheels work together, there being 32 cogs on 
 one and 36 on the other. The larger wheel makes 24 revolu- 
 tions per second. How often will the same cogs come in con- 
 tact in one hour ? 
 
 86. The ratio of the rates at which A and B can walk is aj 
 4 to 5, and the distances they have to go are as 6 to 5. What 
 will be the ratio of the times that they take ? 
 
e> 
 
 %. 
 
 v<>, 
 
 ^ 
 
 or\^ 
 
 IMAGE EVALUATION 
 TEST TARGET (MT-3) 
 
 
 ^^. 
 
 
 V.A 
 
 1.0 
 
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186 
 
 EIGHTH DEPARTMENT. 
 
 
 87. At $125 per acre what is the value of a farm 240 rods long^ 
 and 90 rods vide ? 
 
 88. What is the cost of 50 boards, each 12 feet long, 8 inches 
 wide, and 1^ inches thick, at 4^ cents per foot, board measure ?' 
 
 89. A postman delivered daily for a period of 42 days 4 
 letters more than en the previous day. The aggregate delivery 
 for the last 18 days was the same £..» that for the first 24 days. 
 How many letters did he deliver altogether ? 
 
 90. By selling an article for $5 less than its value I lose J%, 
 Had I sold it for $6 more than I did what would I have gained 
 per cent ? 
 
 PAPER X. 
 
 91. A mixture of 432 gallons of wine and water is in the pro- 
 portion of 7 to 1. How much water must be added that the 
 proportion may be as 6 to 1 ? 
 
 92. A merchant marks goods at an advance of 37^% on cost, 
 and allows a customer a reduction of 10% from his bill. Find 
 the amount of that bill if the merchant makes a profit of ^9.90' 
 on the transaction. 
 
 93. A man hired for a year and was to receive $168 and 5 
 cords of wood. He left at the end of 7| months and received 
 $98 and the wood. Find the price of the wood per cord. 
 
 94. A grocer bought 100 loads of potatoes of 30 bushels, 
 each at 37^ cents a bushel. Allowing 7^ bushels for waste, 
 how much will he gain by selling the rest at 15 cents a peck ? 
 
 95. Write down all the common measures of 720 and 1008' 
 and find their sum. 
 
 96. What number must be added to 20009 to make it exactly 
 divisible by 201 ? 
 
 97. Find the average of 243, 1001, 32, 407, 63, 82, 943, 822,. 
 1001, and 396. 
 
 98. Multiply 3001004 by ^ and divide the product by ^. 
 
EXAMINATION EXERCISES. 
 
 187 
 
 rods long^ 
 
 , 8 inches 
 measure ?' 
 
 2 days 4 
 
 ! delivery 
 
 24 days. 
 
 lose ^%. 
 i^'e gained 
 
 . the pro- 
 that the 
 
 on coat, 
 
 11. Find 
 
 of $9.90 
 
 58 and 5 
 received 
 I. 
 
 bushels. 
 >r waste, 
 peck ? 
 
 md 1008 
 t exactly 
 )43, 822,. 
 
 99. Divide $4.09 between two boys so that one will receive 
 40 cents more than twice what the other receives. 
 
 100. A clock which loses 3 minutes in 12 hours is 20 minutes 
 fast at noon on Monday. What o'clock will it indicate at 6 
 o'clock on Thursday morning ? 
 
 PAPER XI. 
 
 101. A train 90 yards long moving at the rate of | mile a 
 minute meets another train moving half as fast again, and passes 
 it in 6^w seconds. Find the length of the last train. 
 
 102. A Joy bought 15 pecks of nuts at 75 cents a peck and 
 sold them at 10 cents a quart. How much did he make ? 
 
 103. A man buys a house for $8000. The taxes, insurance, 
 etc., during the year amount to $375. He rents the house for 
 $37 a month, and at the end of the year sells it for $50 less than 
 he paid for it. How much did he gain by the transaction ? 
 
 104. The total increase of shipping at Quebec in a certain 
 year was 1.7%. The decrease in the number of sailing vessels 
 was 4.(>%, and the increase in the number of steamers was 
 10. 7 % . Compare the number of steamers and sailing vessels. 
 
 105. A merchant bought goods and paid a certain import duty 
 on them. He then marked them so as to gain I of the total 
 cost, but was obliged to throw off j'^ of this marked price, conse- 
 quently his gain was only Jg of the first cost of the goods. What 
 fraction of the first cost was the duty ? 
 
 106. What is the greatost unit of time with which 15 hours 
 12 minutes and 1 day 3 nours 33 minutes can be expressed as 
 whole numbers ? 
 
 107. A started to walk from Cobourg to Toronto, a distance 
 of 70 miles, at the rate of 5 miles an hour, and at the end of 
 every hour he rested 15 minutes. Two hours after A started B 
 set out to drive from Cobourg to Toronto at the rate of 7 miles 
 an hour, and at the middle of the journey he rested 2 houra. 
 How long after B reached Toronto did A arrive there ?, 
 
BSSBBl 
 
 188 
 
 EIGHTH DEPARTMENT. 
 
 108. It costs 20 cents a line to insert an advertisement in a 
 newspaper the first time, 6 cents a line ft)r each of the 10 subse- 
 quent insertions, and then 2| cents a line. If a man is charged 
 ^.80 for a space of 6 lines, how often should his advertisement 
 appear ? 
 
 109. If I were to put posts 6 teet instead of 7 feet apart 
 around a field I should require 66 posts more. The field is 40 
 rods one way. How many acres does it contain ? 
 
 110. A merchant buys goods at a discount of 30% and 10% 
 from the list price, and sells at 25 % and 5 % from the list price. 
 "What per cent does he gain ? 
 
 PAPER XII. 
 
 111. How much gold 90% pure must be mixed with 24 ounces 
 (J5% pure so that the mixture may be 80% pure ? 
 
 112. The interest on a certain sum for 6 years is $261, and 
 the true discount for the same time is $180. Find the sum and 
 the rate. 
 
 113. The sum of the interest, amount, true discount, and 
 present wortn is $2400. The principal is $1000. What is the 
 interest ? 
 
 114. A merchant bought 240 yards of tweed and 1560 yards 
 of flannel, the price of the flannel per yard being j\ that of the 
 tweed per yard. He sold the tweed at a gain of 25% and the 
 flannel at a loss of 20 % , losing on the whole $30. Find the cost 
 of the tweed per yard. 
 
 115. When stock is boufrht at a discount of 20% and sold at a 
 discount of 16 % what per cent is gained ? 
 
 116. A has 37|% less money than B. B has how much per 
 cent more than A? 
 
 117. A 27-gallon keg is half full of wine § pure ; 10% is drawn 
 out and the keg filled with water. What is the percentage of its 
 purity now ? 
 
EXAMINATION EXERCISES. 
 
 
 189 
 
 118. A merchant sells goods at 25% profit and takes eggs afc 
 market value in payment. If one egg in each dozen is bad, what 
 is his percentage of net gain ? 
 
 119. i real estate agent gets $95 for selling a house and lot 
 for $4750. What is his rate of commission ? 
 
 120. Two pounds of tea and 6 pounds of sugar cost $2.20; if 
 sugar wera to rise 50% and tea 10% they would cost $2.66. 
 Find the price per pound of tea and sugar. 
 
 PAPER XIII, 
 
 121. Stock bought at 10% premium pays 6% on the invest- 
 ment. What ?.er cent would the same stock pay if bought at 
 17 % discount / 
 
 122. The interest of a certain sum of money for 2^ years at 7 % 
 is $5.87^. What is the true discount on the same sum for the 
 same time and at the same rate ? 
 
 123. I have to be at a certain place at a certain time. I find 
 that if I walk at the rate of 3 miles an hour I shall be 20 minutes 
 too late, and if at the rate of 5 miles an hour I shall be 12 
 minutes too early. How far have I to go ? 
 
 124. What integer multiplied by the next greater gives a pro- 
 duct of 1980 ? 
 
 126. How many shares of stock must be sold at 7% discount 
 to realize $6510 ? 
 
 126. One vessel, M, contains a mixture of 27 gallons of wine 
 and 11 of spirits. Another vessel, N, contains a mixture of 4.3 
 gallons of wine and 14 of spirits. Compare the strength of the 
 two mixtures, supposing the strength of spirits to be three times 
 that of wine. 
 
 127. I sold a farm for $5600 and gained as much per cent as 
 the farm cost me. Find the cost. 
 
 128. What was the face of a draft bought for $1970 when 
 exchange was at 1^% discount? 
 
 
190 
 
 EIGHTH DEPARTMENT. 
 
 129. A publisher wishes to net 14 shillings on each copy of a 
 work. What price should he put upon it that he may be able to 
 allow the trade 30% discount? 
 
 130. A man undertakes to build a house in 24 days. He 
 employs 200 men to work 9 hours a day. At the end of 16 dr n 
 the work is but one-half done. How many additional hands 
 must he employ so that by increasing the day's work to 10 hours 
 he may have the work completed at the end of the 24 days ? 
 
 M 
 
 ^.r 
 
 PAPER XIV. 
 
 131. Sold f of &n article for what ^ of it cost. What was the 
 gain per cent ? 
 
 132. In what time will a $1700 note drawing 7^ % simple in- 
 terest double itself ? 
 
 133. A farmer has 434 sheep in 3 fields. Two-thirds of the 
 number in the first field equals | of the number in the second, 
 and f of the number in the second equals | of the number in the 
 third. How many are in each field ? 
 
 134. Two-thirds of A's money is to | of B's as 3 to 4. To- 
 gether they have $1520. How much has B ? 
 
 135. Two lots of cloth which together amount to 204 yards 
 a.re in length as 8 to 9, and in price as 10 to 11. Their total 
 value is £134 53. Find the separate quantities and the prices 
 per yard. 
 
 136. One side of an avenue is planted with maples 20 feet 
 apart and the opposite side with balsams 28 feet apart. How 
 many times will a maple be found directly opposite to a balsam 
 in 7 miles ? 
 
 137. What is the least number of even bushels of grain that can 
 be exactly measured by a 3-quart, a peck, or a 5-gallon measure ? 
 
 138. On a bill of $78 having 8 months to run the true d"s- 
 -count is $6. On a bill of $85 the true discount at the same rate 
 is $5. How long has the latter bill to run ? 
 
EXAMINATION EXERCISES. 
 
 191 
 
 139. Five men agreed to do a piece of work, but two of the 
 men did not come, and as a consequence the work was pro- 
 longed 3^ days. In what time could the 5 men have done the 
 "Work ? 
 
 140. A man after a tour in Switzerland found that he had 
 «pent each day half as many shillings as the total number of 
 days he had been away from home. His tour cost £67 12s. 
 How many days did it occupy ? 
 
 PAPER XV. 
 
 141. A merchant sells his goods at a profit of 15%. What 
 amount of goods must he sell to gain $2700 ? 
 
 142. If a town pays its tax collector 5%, and allows 6% for 
 uncollected taxes, what should be the amount of taxes levied to 
 realize $36,100? 
 
 143. A and B do a piece of work for $36. They agree to 
 divide the money in proportion to their ability to work, uhich 
 IS as 2 to 3, and also to the time each worked, which is as 3 to 4. 
 How much money should each get ? 
 
 144. For what must good," worth $19,100 be insured at ^% 
 so that in case of loss the worth of the goo(^. and the premium 
 may be recovered ? 
 
 145. If 5 men and 7 boys can reap a field of corn of 125 acres 
 in 15 days, in how many days will it take 10 men and 3 boys to 
 reap a field of 75 acres, each boy's work being equal to A of a 
 man's ? 
 
 146. A sold goods which cost him $300 to B at a certain rate 
 of profit. B sold the same goods to C at the same rate of profit. 
 C paid $432 for the goods. What did B pay for them ? 
 
 147. A man both in buying and selling cheats 10% by means 
 of false scales. Find his fraudulent gain per cent on produce 
 bought and sold. 
 
 148. If stock bought at 10% discount pays 5% on the invest- 
 ment, at what price should the same stock be bought to pay 6% ? 
 
192 
 
 EIGHTH DEPARTMENT. 
 
 ^ 
 
 149. In a liquid mixture there are 12 gallons of wine to 5 gal- 
 lons of water. On the addition of 20 gallons of water the pro- 
 portion is 4 gallons of wii.e to 3 gallons of water. What quan- 
 tities were in the original mixture ? 
 
 150. An estate agent bought two houses. The first cost | a» 
 much as the second. In selling he gained 20% on the first and 
 lost 5% on the second. His net gain was ^160. Find his net 
 gain per cent. 
 
 PAPER XVI. 
 
 151. How many rods of fence will be required to enclose 2560 
 acres of land in a scjuare form ? 
 
 152. A and B together Jiave $136, and § of A's money is equal 
 to I of B's. How much has each ? 
 
 153. A grocor gained 25% by selling 12 pounds of sugar for & 
 dollar. How much par cent will he gain by selling 15 pounds 
 for one dollar ? 
 
 154. Divide $240 among A, B, and C so that A may have $140 
 more than B and twice as much as C. 
 
 156. If the cost of an article had been 8 % less the gain would 
 have been 10% more. Find the gain per cent. 
 
 156. From a cask of wine worth $1.20 a gallon ^ part is 
 drawn and replaced by wine worth 80 cents a gallon. WL.tt is 
 now the value per gallon of the wine in the cask ? 
 
 157. In walking 18 miles a man finds that the distance he 
 walks in 100 minutes is f of the remaining distance. What is 
 his rate of walking '( 
 
 158. Find the cost of fencing a rectangular field of 3^ acres of 
 smallest possible perimeter at $1.50 a rod. 
 
 159. Thirteen hundred workmen in a factoiy are placed in 
 charge of four superintendents, A, B, C, and D. For every 4 
 men under A there are 5 under C, and for every 9 under B there 
 are 10 under D, and for every 2 under A there are 3 under B. 
 How many "je under each 'i 
 
EXAMINATION EXEKCISES. 
 
 103 
 
 160. In the Centigrade thermometer the freezing point is zero 
 and the boiling point is 100°; in Fahrenheit's the freezing point 
 IS 32° and the boiling point is 212°. What degree C. corresponds 
 
 PAPER XVII. 
 
 161. In 1880 February had 5 Sundays. When will this occur 
 again ? 
 
 162. A boy rowed 2^ miles up a stream and back again in 1 
 hour and 40 minutes. He rowed down three times as fast as he 
 rowed up. Find his rate of rowing in still water i 
 
 163. When it is noon at Greenwich it is 7 o'clock a.m. at 
 Philadeli>hia. What is their difference of longitude? 
 
 164. A square courtyard is bordered by a gravel drive 10 
 yards wide, and the drive covers 4000 square yards. How many 
 square yards in the enclosed grass plot ? 
 
 166. Find the cost of excavating a cellav 6 feet deep for n 
 house 20 feet by 30 fest, at 10 cents per cubic yard for the first 
 foot in depth, 12 cents for the second, 15 cents for the third, 16 
 cents for the fourth, 18 cents for the fifth, and 20 cents for the 
 sixth. 
 
 166. What fraction of the area of the floor of a room 35 feet 
 square would be left uncovered by 147 yards of carpet 30 inches 
 wide? 
 
 167. A contractor found that it would take 16 men 6 weeks to 
 finish a piece of work. He decided to have it done in 8 days. 
 How many men should he employ ? 
 
 168. Three men own altogether 21,950 sheep; | of the number 
 owned by the first, % of the number owned by the second, and f 
 of the number owned by the third are equal. How many sheep 
 has each ? « 
 
 169. A society collected for charitable purposes a fund of £960. 
 Each member paid as many pence as there were members in the 
 whole society. How many members were there ? 
 
 N 
 
mi 
 
 194 
 
 EIGHTH DEPAUTMENT. 
 
 170. I held two notes, each due in 2 years, the aggregate face 
 value of which wtts $1020. One was discounteil at 5% bank dis- 
 count and the other at 6% true discount. The total i)roceed8 
 was $923. What was the face value of each ? 
 
 PAPER XVIII. 
 
 171. A cubic foot of water weighs 62^ pounds, and a floating 
 body displaces its own weight jf water. How many cubic feet 
 of water will be displaced by a ship and cargo neighing 500 tons ? 
 
 172. A miller exchanges flour worth $5.40 per barrel with a 
 farmer for hay worth $9 per ton. If the farmer asks $10.60, 
 what price should the miller put on the flour ? 
 
 173. Two trains start at the same time from London and 
 Exeter and proceed towards each other at the rates of 24 and 32 
 miles an hour respectively. When they meet it is found that 
 one train has run 24 miles more than the other. How far is it 
 from London to Exeter ? 
 
 174. If I sell my horse for £62, and my carriage for £26, I 
 shall gain 10% on the original coat of both ; but if I sell the horse 
 for £63, and the carriage for its original cost, I shall lose 10 % . 
 Find the original cost of each. 
 
 175. A cistern is 10 feet wide by 12 feet long, and the water 
 in it is 8 feet deep. If a rectangular stone 3 feet by 2 feet by 1 
 foot be dropped into the cistern, how much will the Avater rise ? 
 
 176. A merchant deducts 20% from the marked price of his 
 goods and still makes a profit of 16%. At what advance on cost 
 are the goods marked ? 
 
 177. It costs $800 to fence a farm 80 rods square. How much 
 more will it cost to fence a farm of equal area in the form of a 
 rectangle four times as long as it is wide with the same kind of 
 fence ? 
 
 178. A room is 8| yards long and 6J yards wide. It costs 
 $12.60 to cover the walls with paper 2 feet wide and costing 7 
 cents a yard. Find the height of the walla. 
 
EXAMINATION EXERCISES. 
 
 195 
 
 179. A. can do a piece of work in 8 days when B helps him 5 
 days ; B can do the work in !> days when A helps him 5 days. 
 How long will the work take both when working together? 
 
 180. A starts from Belleville for Trenton at the same time 
 that B starts from Trenton for Belleville. They arrive at their 
 destinations respectively 40 min-.tes and (K) minutes after meeting 
 ■eacii other. Compare their rates. 
 
 PAPER XIX. 
 
 181. A, B, and C do a piece of work for which $110 is paid. 
 Working alone it would take A 1| times as long a« B and C 
 together, and B 2^ times as long as A and C together. How 
 should the money be divided ? 
 
 182. A person's income is derived from the commission on 
 £6975 at a certain rate per cent, and on £5300 ut 1% more than 
 the former rate. His whole income is £547. Determine the 
 rates. 
 
 183. A factory tailor can make 5 shirts in 2 hours ; whether 
 will it be more profitable for him to be paid at the rate of 18 
 cents an hour 
 
 8 pipes. A, B, and C. By A and B 
 
 ': minutes, and emptied by C in 90 
 
 -n together empty the cistern in 3 
 
 ) cistern be filled when all three are 
 
 a shirt ? 
 
 184. A cist 
 together it can 
 minutes. A an 
 hours. In v,rhat tiu: 
 open together ? 
 
 185. I received 9% dividend on stock purchr,aed at 40% dis- 
 count. What per cent did my investment pay { 
 
 186. What capital should be invested in 5% stock at 96J to 
 produce the same income as £2321 invested in 3% stock at 77 ? 
 
 187. What is the amount of a note due in 8 months at 4|% 
 if the ditference between the true and the bank discount is 9 
 ^shillings ? 
 
 188. What principal will amount to $455.65 in 7 A years at 4% 
 simple interest ? 
 
t-^-^-. 
 
 19G 
 
 EIGHTH DKPAKiiENT. 
 
 189. B can beat A by ^ a mile in a course of 4 miles. can 
 beat B by 2 minutes and A by 1 mile over the same course. ^ 
 Fiml the rate per hour of A, B, and C. 
 
 190. In arranging the terms of a partnership A ha** a note of 
 $420 not bearing interest. B lias a similar note of #346 but 
 having three times as long to run. A is willing to allow 3-300 
 for B's note. How much should B allow for A's ? 
 
 PAPER XX. 
 
 191. A traveller on a train notices that 2| times the number 
 of spHces between the telegraph poles that he passes in a minute 
 
 x the rate of the tmin in miles per hour. How^ t. • apart are 
 the poles ? 
 
 192. A merchant purchased a number of pounds o! tea for 
 $12. Hciu hfc bought 10 pounds more he would huve been 
 allowed a discount of 10% on the whole, and the price would 
 have been $18. How many pounds did he buy at first? 
 
 193. The prices of seats at a lecture v^ere 50 cents, 35 cents, ' 
 and 26 cents. It was known that for every 3 seats sold at 3& 
 cents there were 4 sold at 25 cents, and for every 3 sold at 60 
 cents there were 4 sold at 36 cents. The whole sum realized 
 from the sale of seats was $76.20. How many 26-cent seats, 
 were sold I 
 
 194. The government map of Manitoba is drawn to a scale of 
 6 miles to the inch. What length of line on the map will repre- 
 sent one side of a square farm containing 160 acres ? 
 
 195. A woman bought a certain number of yards of c'res» 
 goods at $1 a yard, and half as many yards of lining at half aa. 
 much a yard. The cost of the whole was $12.50, How many 
 yards of each did she buy ? 
 
 196. An article was sold at a price which was ^ above cost. 
 } .,d the cost been f of what it really was, and the selling price 
 remained the same, the gain would have beeu $3. Find th& 
 first cost. 
 
EXAMINATION EXK*?:* ijjijj. 
 
 197 
 
 197. There were tro trains, one 210 feet and the other 230 
 feet long. Wh^m going on parallel tracks in the same direction 
 <>ne passed the other in 16 seconds. When going in opposite 
 directions they passed in 3| seconds. How many miles an \ jur 
 were they moving ? 
 
 198. A customer bought what he supposed was $46 woxth of 
 tea, but a false weight having been used he got only U2 vorth. 
 H<»w many ounces were given him for a pound ? 
 
 199. Show why 8 must be a factor of the product of a.iy two 
 consecutive even numbers. 
 
 800. A dealer imported 50 chests of tea containing 30 pounds 
 each and invoiced at 45 cents a pound He paid a duty of 15% 
 on the invoiced price and $17.60 freight. When he unpacked 
 the tea he found that 5 chests we^a damaged so that ho had to 
 sell th^m for 50 cents a pound . what price per pound must 
 he cell the remainder to gain 20;^ on his entire outlay ? 
 
 
 PAPER XXI. 
 
 201. If T buy for 10% less I shall gain 16% more. What is 
 my rate ot gain ? 
 
 202. A, B, and C are partners. A receives 35% of the profits. 
 Of the remainder B's share is G0% more than C's. C's income 
 is increased by $150 when the profits rise from 10% to 12%. 
 Pind the sum invested by each. 
 
 203. A speculator bought a piece of land at $1500, and after- 
 wards sold it for $1795.40. The buying and selling were done 
 through a broker, who charged 2% for each transaction. Find 
 the speculator's actual gain per cent on the entire cost. 
 
 204. How many pounds of tea at 64 cents a pound must a 
 grocer mix with 4 pounds at 82 cents a pound that he may sell 
 the mixture at 96 cents a pound and gain 33^% on his outlay ? 
 
 205. A Darrel of sugar containing 280 pounds cost $21. In 
 weighing it out it lost 5%. What per cent is gained by selling 
 it at 10| cents a pound ? • 
 
198 
 
 EIGHTH DEPARTMENT. 
 
 206. Bought 2000 pounds of sugar, part at 7 cents a pound 
 and part at 10 cents a pound. Had I bought the whole at 8 
 cents a pound it would have cost me ^13 less than I paid for it. 
 How many pounds of each kind did I buy ? 
 
 207. How much did the creditors receive on the ^, the account 
 of a bankrupt estate being as follows : — 
 
 Goods valued at $3500, sold at 62ic. on the 8 ; 
 
 Book debts amounting to $1750, sold at 55c. on the $ ; 
 
 Notes receivable amounting to $680, sold at 80c. on the $ ; 
 
 Expenses, 2 % of the total sum realized ; 
 
 Liabilities, $2350, $750, $1300, $1365, and $724.50? 
 
 208. When currency is at a discount of 40% what is the cor- 
 responding premium on gold ? 
 
 209. Find the cost of digging a drain 48 rods long, 3 feet deep, 
 3^ feet wide at the top, and 2^ feet wide at the bottom, at 4 cents, 
 a cubic yard. 
 
 210. If sterling exchange is quoted at $4.84, and exchange in. 
 London on Frankfort is at 20.25 marks per £, what ehould a bill 
 of 3800 marks be worth in New York ? 
 
 PAPER XXII. 
 
 211. If gold is at 12i% premium, what is the corresponding 
 discount on curre:.cy? 
 
 212. If I of the selling price is 20% less than the cost, what is 
 the gain per cent ? 
 
 213. A piece of work was to be performed by 6 ftien in a cer- 
 tain time ; 2 men, however, failed to come, and the work was. 
 consequently prolonged 6 days. In what time should it have 
 been done ? 
 
 214. A grocer intending to gain 20% on his stock of tea fixed 
 his prices accordingly. After selling 5~ of his stock he was forced, 
 to reduce his price 10 cents per pound, and so gained only 14| % 
 on the whole. Find the cost price per pound of the tea. 
 
EXAMINATION EXERCISES. 
 
 199 
 
 216. How many thousand feet, board measure, are there in 
 100 sticks of square timber each 30 feet long and 16 inches by 
 15 inches at the ends ? 
 
 216. A certain sum of money if invested in 6% stock at 90 
 purchases $400 more stock than if invested in 7% stock at 96. 
 Find the difference of income. 
 
 217. A man drove to town at the rate of 8 miles an hour, and 
 after remaining there 28 minutes he i -turned at the rate of 5 
 miles an hour. He was absent 6 hours. How far was he from 
 town ? 
 
 218. A train started to go from P to Q, 210 milos, at 30 miles 
 an hour, but after having gone 100 miles it was delayed 20 
 minutes by an accident. It finished the trip at 22 miles an hour. 
 How much behind time was it ? 
 
 219. If I ask 30% profit on an article, but fall 10% on my 
 asking price, what rate of profit do I make ? 
 
 220. I received an 8 % dividend on stock at 80. I invested 
 ray dividend in the same stock and then had $6875 stock. Find 
 my dividend. 
 
 PAPER XXIII. 
 
 221. A merchant buys a quantity of svrup for $750. By 
 using a false measure and by marking at 35% gain he nets $375. 
 What fraction will express the size of his measure ? 
 
 222. A merchant buys sugar at 8 cents a pound and sells it at 
 a profit of 25%, but by mistake uses a pound weight Jj too 
 heavy. Having sold all his sugar he finds he has lost $16 by 
 overweight. How many pounds did he buy ? 
 
 223. A sold B a carriage which cost him $150 at 12i^ % profit. 
 B sold it to C at a profit of 10%. What would have been A's 
 profit per cent if he had sold to C for the price C paid ? 
 
 224. A person makes a journey 1248 miles in 12 days, going 
 13 hours a day. In how many days of 9 hours will it take him 
 to go 576 miles at the same rate ? 
 
200 
 
 EIGHTH DEPARTMENT. 
 
 225. A can do aa much work in 3 hours as B can do in 5 
 hours. How long will it take A lo finish a piece of work of 
 which B has done | in 20 days ? 
 
 226. The wages of A and B together for 7^ days will pay the 
 wages of A alone for 20 days. For how many days will this sum 
 I)ay the wages of B alone ? 
 
 227. A farmer sold 14 bushels of wheat and 16 bushels of oats 
 for $13.62. He received for the wheat 32 cents a bushel more 
 than for the oats. Find the price ot ^ach per bushel. 
 
 228. If a grocer sells a tub of butter at 22 cents a pound he 
 will gain 108 cents, but if he sells at 17 cents a pound he will 
 lose 112 cents. Find the weight of the tub and the cost per 
 pound. 
 
 229. At what tim^ between 10 and 11 are the hands of a 
 clock together ? 
 
 230. A can do i of a piece of work in 2 hours ; B can do ^ of 
 the remainder in 3 hours, and C can do the remainder in 4 hours. 
 How long will the work take them if all work together ? 
 
 PAPER XXIV. 
 
 231. One man walks 2^ miles in 35 minutes, and another 
 walks 4| miles in 60 minutes. How much of a start must the 
 slower have so that in a race of 7^ miles they may come in 
 even ? 
 
 232. The H. C. F. and L. C. M. of two numbers between 100 
 and 200 are C and 3150. Find the numbers. 
 
 233. How far will a carriage have traveled when the fore 
 wheel will have turned 60 times more than the hind wheel, the 
 circumferences being 8 feet and 10 feet ? 
 
 234. A garrison has provisions for 60 days. After 12 days a 
 reinforcement of 3000 men arrives. By putting the men on half 
 rations the provisions are made to last 32 days longer. How 
 many men in the original garrison ? 
 
EXAMINATION EXERCISES. 
 
 201 
 
 236. A grocer spent equal suras in buying tea, corfee, and 
 sugar. He gained 20% on the tea, 10% on the coffee, and lost 
 8% on the sugar. His total receipts were $3864. Find the cost 
 of each. 
 
 236. Two-fifths of a mixture of wine and water is wine, but 
 when 10 gallons of water are added the wine is only ^^ of the 
 whole. Find the quantities at first. 
 
 237. Add together the 40 numbers beginning with 1002. 
 
 238. Three-fourths of the difference between two numbers is 
 «qual to ^ of their sum. The smaller number is 287. Find the 
 larger. 
 
 239. The difference between the simple and the compound 
 interest of a certain sum at 8% for 2 years is $1.20. Find the 
 sum. 
 
 240. How many pounds of butter must be mixed with 12| 
 pounds of lard that the mixture may contain 33^% of butter ? 
 
 PAPER XXV. 
 
 241. What number multiplied by ^\ of itself will give 1188 ? 
 
 242. A man engaged with a farmer at $1.10 a day for each of 
 90 days that he worked. He promised to forfeit 60 cents for 
 each idle day. At the end of the time he received $61.60. How 
 many days did he work ? 
 
 243. A boatman can row 10 miles an hour in still water. In 
 going a certain distance down a stream which runs at the rate of 
 2 miles an hour it takes him 10 hours. How long will it take 
 him to row back ? 
 
 244. Find the time between 8 and 9 when the minute hand of 
 a clock is 7 minute spaces behind the hour hand. 
 
 246. An agent sold wheat at 4% commission and invested the 
 proceeds, less his double commission, in sugar. He received 2% 
 commission on the actual sum invested, and his whole commis- 
 : sion was $63. Find the cost of the sugar ? 
 
202 
 
 EIGHTH DEPARTMENT. 
 
 246. How much does a grocer who gives only 16§ ounces for 
 a pound cheat a customer who buys goods amounting to $64 ? 
 
 247. A starts to walk from one town to another at the average^ 
 rate of 3 miles an hour. Twenty minutes later a bicyclist, B, 
 starts on the same journey at the rate of 12 miles an hour. On 
 reaching the second town B rests ^ of an hour, and after riding 
 20 minutes on his return journey meets A still on his way. 
 What is the distance between the two towns ? 
 
 248. The assessed value of the property in a town is $3,265,- 
 000, and the tax to be raised is $39, 180. What will be the rate 
 on the $, and what will be the amount of A's taxes, his property 
 being assessed at $15,000 ? 
 
 249. A can do as much work in 2 days as B can do in 2^, and 
 B can do as much in 2 days as C can do in 2^. They all start 
 together and complete a job worth $61. How much of the 
 money should A receive ? 
 
 250. A St. Paul investment company declared a dividend of 
 8%, and one of the shareholders, who lived in Toronto, drew on 
 St., Paul for his money. He received $318.40, the rate of ex- 
 change being ^% discount. Find how many shares this man 
 owned. 
 
 PAPER XXVI. 
 
 261. If a parcel of 12 pounds weight is carried 80 miles by rail 
 for 2s. 4d. , and the rate for the distance over 50 miles is f of the 
 rate for the first 50 miles, how far can a parcel of 8 pounds be 
 carried for 4d.? 
 
 252. There are 3 sections of land in such a shape that the 
 length is 6 times the breadth. The whole is divided into 96 
 rectangular lots, each of which is twice as long as it is wide. 
 Find the dimensions in rods of each lot. 
 
 253. If 1 sell one of my two farms for $4500 and the other 
 for $1800 I will gain 5 % on the cost of both ; but if I sell the 
 dearer farm at $4000 and the other at cost I will lose 5%. Find 
 the cost of each farm. 
 
EXAMINATION EXERCISES, 
 
 203 
 
 264. A mixture of black and green tea is worth $22.65. An- 
 other mixture with the proportions interchanged is worth $24.60. 
 Four pounds of black tea cost as much as 5 pounds of green. 
 Find the cost price of each per pound. 
 
 255. A merchant bought a certain number of yards of olcth 
 at $2.50 per yard. He sold f of the cloth a^ 25% profit, and on 
 the sale of the remainder he lost $15. If his total loss was equal 
 to 5 % , find the number of yards. 
 
 266. A and B buy the apples in a barrel for $2.25. B pays 
 75 cents of this price, A paying the remainder. It costs B 25 
 cents to deliver the apples, and A gives 15 cents for the barrel, 
 which B keeps. If they share the apples equally, who owes the 
 other, and how much ? 
 
 267. An agent sells flour on commission of 2%^ and purchases 
 goods on true commission of 3%. if he had received 3% for 
 selling and 2% for buying his whole commission would have 
 been $6 more. Find the value of the goods bought. 
 
 258. The owner of a mill driven by water power got an insur- 
 ance on it at the rate of 1^%. He afterwards introduced steum 
 power, and the company took an additional risk of $1200. They, 
 however, raised the rate ^% on account of the greater danger. 
 The extra premium required amounted to $53.50. For what 
 amount was the mill first insured ? 
 
 259. A railway train, after travelling for 1 hour, has an acci- 
 dent which delays it 60 minutes, after which it proceeds at f of 
 its former speed and arrives at its destination 3 hours behind 
 time. Now, had the accident occurred 50 miles further on the 
 train would have arrived If hours sooner. What is the length 
 of the line ? 
 
 260. A rectangular court is 50 yards long and 30 yards broad. 
 It has paths joining the middle points of the opposite sides, each 
 6 feet wide, and a path of the same breadth running all around 
 it. The remainder is covered with grass. The cost of the pave- 
 ment was 12^ cents per square foot, and of the grass 70 cents per 
 square yard. What was the cost of laying out the court ? 
 
204 
 
 EIGHTH DEPARTMENT. 
 
 PAPER XXVII. 
 
 2S1. A man's income is derived from the proceeds of $2275 at 
 a certain rate per cent, and $2710 at 1 % more than the former 
 rate. His whole income is $463. What are the rates ? 
 
 262. xV boy can split a cord of wood in 3 hours and pile a cord 
 in 45 minutes. How long will it take him to split and pile 6 
 cords ? 
 
 263. The time occupied by a train 352 yards long, going at 
 the rate of 40 miles an hour, in crossing a bridge is 50 seconds. 
 Find the length of the bridge. 
 
 264. A man sells goods for $1125. Half he sold at an advance 
 of 25 % on the cost, f at an advance of 12^ % , and the remainder 
 at J of the cost. What did he pay for the goods ? 
 
 265. Equal weights of gold and silver are in value as 20 to 1, 
 and equal \olumes are in value as 1284 to 35. A certain volume 
 is composed of equal weights of gold and silver. Find how many 
 times more valuable the same volume would be wei. ., it composed 
 wholly of gold. 
 
 266. A person buys a horse upon borrowed money, for w^hich 
 lie pays 6% per annum. The horse earns 70 cents a day and 
 costs 1% of his purchase price for daily keeping. The owner 
 sells him at the end of a year for $50 and realizes $132.40 upon 
 the whole transaction. What did the horse cost ? 
 
 267. A man owns a horse and a saddle ; ^ of the value of the 
 horse is equal to 4 times the value of the saddle ; the horse and 
 saddle together are worth $170. Find the value of each. 
 
 268. By selling an article for $21 1 lost i2h%. At what price 
 ahtjuld I have sold it in order to gain 12^ % ? 
 
 269. The pendulum of one clock makes 24 beats in 26"; that 
 of another 36 beats in 40". If they start at the same time, when 
 first will the beats occur together ? 
 
 270. What is the market price of 5 % bank stock which yields 
 6 % interest after an income tax of 3 % has been paid ? 
 
EXAMINATION EXKRCiSES. 
 
 205 
 
 PAPER XXVIII. 
 
 271. A peraon sells a certain amount of 5% stock for 86 and 
 invests in 6% at 103, and by so doing changes his income by $1. 
 Is the change an increase or a decrease ? How much stock did 
 he sell 'i 
 
 272. T-ead is 11.4 times and zinc 7.2 times as heavy as water. 
 If 3 pounds of lead and 2 pounds of zinc be melted together, 
 compare the weight of the mixture with that of water. 
 
 273. I found that by giving 13 cents each to a certain number 
 of beggars I would have just 10 cents left, but by giving each of 
 them 17 cents I would not have onough by 10 cents. How many 
 beggars were there ? 
 
 274. A contractor found that he would have $75 left if he 
 paid iiis men 85 cents each, but that he would need $125 more 
 if he paid them $1.25 eacli. How many men were there ? 
 
 276. A boy earned 15 cents a day for prompt attendance dur- 
 ing the 200 school days in the year, and forfeited 12 cents each 
 day he was tardy. At the end of tlie year he received $29.73. 
 How many days v/as he punctual ? 
 
 276. A crew can row up a stream a certain distance in 64 
 minutes and back again in 60 minutes. Determine the distaijice, 
 the rate of the stream being half a mile an hour. 
 
 277. Two-thirds of a number increased by I of the number, 
 and this increased by 34, will give twice the number. Find the 
 number. 
 
 278. When the hour hand of a clock is 22 minutes ahead of 
 the minute hand, how far must the minute hand move to over- 
 take the hour hand ? 
 
 279. If the time past noon increased by 90 minutes equals ^ 
 of the time from noon till midnight, what time is it ? 
 
 280. When wheat is worth 90 cents a bushel a baker's loaf 
 weighs 9 ounces. How niany ounces should it weigh when wheat 
 is worth 72 cents a bushel ? 
 
-206 
 
 EIGHTH DEPARTMENT. 
 
 PAPER XXIX. 
 
 281. A pound of tea and 7 pounds of sugar cost ^l.C4. If 
 sugar were to rise 60% and tea 25% they would coat ^.33. 
 Find the price per pound of tea and sugar. 
 
 282. A person sells 184 shares of 4 % stock at 92 and invests 
 in 3^% stock, gaining $100 per annum by the change of income. 
 At what price did he purchase the latter stock ? 
 
 283. In erecting a house I paid three times as much for mate- 
 rial as for labor. Had I paid 6 % less for the material and 4 % 
 more for the labor the house would have cost me $2334. What 
 did the house cost ? 
 
 284. How many pounds of coffee at 24 cents must a merchant 
 mix with 6 pounds at 30 cents that he may sell the mixture at 
 40 cents and gain 33 J % ? 
 
 285. Four pipes, A, B, C, and D, fill a cistern in 3, 12, 15, and 
 20 hours respectively. Four other pipes empty it in 4, 10, 30, 
 and 60 hours rebpectively. If the eight pipes ai*e open together, 
 in how many hours will the cistern be filled ? 
 
 286. A person increases his capital 20% annually, less a yearly 
 expenditure of ^600. At the end of four years his capital 
 amounts to $18,052. Find his original capital. 
 
 287. A man bought a piece of cloth at 01.40 a yard and lining 
 for it at GO cents a yard. There were 35 yards altogether, and 
 the total price was $37. How many yards were there of each ? 
 
 288. A certain sum amounts to $2070 in 6 months, and to 
 y( $2420 in 3 years, simple interest. What is the rate per cent ? 
 
 289. How far must a person proceed on a stage which travels 
 4^ miles an hour in order that he may walk back at the rate of 3 
 miles an hour and be gone just 7^ hours ? 
 
 290. A man buys 160 pounds of sugar, and after selling 100 
 pounds finds that he has been selling at a loss of 5%. At what 
 per cent advance on the cost must he sell the remaining 60 
 pounds that he may gain 10 % on the entire transaction ? 
 
EXAMINATION EXERCISES. 
 
 £07 
 
 I 
 
 I 
 
 PAPER XXX. 
 
 291. A lump of gold 22 carats fine contains 36 ounces of alloy 
 How many ounces of alloy in a lump of the same weight only 10 
 ■carats fine ? 
 
 292< Find the smallest multiplier that will make 3428 a per- 
 fect square. 
 
 293. Show without division that 36432 contains 8, 9, and 11 
 AS factors. 
 
 294. How many days elapsed between the annula- eclipse of 
 May 16, 1836, and that of March 15, 1858 i 
 
 296. By selling goods at 60 cents a pound 8% is lost. What 
 -advance must be made in the price in order to gain 15%? 
 
 296. Divide #54.25 among three persons, giving the second 
 -#10 less than the first and twice as much as the third. 
 
 297. A substance is weighed from both anm of a false balance 
 -and its apparent weights are 18 pounds and 8 pounds. Find its 
 true weight. 
 
 298. Wlien the sum of the interest and true discount is sub- 
 tracted from the sum of the true present worth and amount the 
 remamder is $2460. What is the present worth ? 
 
 299. A merchant buys ;;oods at a discount of 40% and 20% 
 from the list prices, and sells at a discount of 10% and 5% 
 What is his gain per cent, allowing 10% of his sales for bad 
 debts ? 
 
 300. X, Y, and Z formed a partnership to carry on a milling 
 business. X owned the site, valued at #1500; Y put up the 
 building, worth #2400; and Z put in the machinery, costing 
 #3000. They ran the mill for one year on this basis, and then 
 agreed to take equal shares in it ; but meantime the value of the 
 land had increased 20%, the value of the building had decreased 
 10%, and the worth of the machinery had depreciated 25%. 
 Who should pay the other, and how much ? 
 
208 
 
 EIGHTH DEPARTMENT. 
 
 PAPER XXXI. 
 
 301. What is a concrete number ? An abstract number ? 
 
 302. Show that a unit is not necessarily a single thing. 
 
 303. Why do we be^'in at the unit's place in the addition of 
 numbers ? 
 
 304. How nmy the accuracy of the process of subtraction be 
 verified ? 
 
 305. Any number is divisible by 9 if the sum of its digits be 
 divisible by 9. Why ? 
 
 306. The product of the greatest common measure and least 
 common multiple of two numbers is equal to the product of the 
 two numbers. Why 'I 
 
 307. C(jmpar9 the metric system of weights and measures with 
 the system in general use. 
 
 308. Prove the rules for multiplication and division of frac- 
 tions. 
 
 309. Show that the true discount of any sum of money is the 
 true present worth of the bank discount for the same time and 
 rate. 
 
 310. Prove that a number will be divisible by 11 if the sum of 
 the digits in the even places differs from that in the odd places. 
 by a multiple of 11. 
 
 m 
 
g- 
 
 Idition of 
 
 action be 
 
 digits be 
 
 md least 
 3t of the 
 
 ires with 
 
 of frac- 
 
 )y is the 
 ime and 
 
 3 sum of 
 d place*