32 What part of 25 is § of an unit ? Ans. 33. If A can do a piece of work alone in 10 days, Bin 20 days, C in 40 days, and D in 80 days; set all four about it together, in what time will they finish it? Ans. 51 days. 34. A farmer being asked how many sheep he had, answered, that he had them in five fields, in the first he had of his flock, in the second, in the third, in the fourth , and in the fifth 450; how many had he? Ans. 1200. 35. A and B together can build a boat in 18 days, and with the assistance of C they can do it in 11 days; in what time would C do it alone? Ans. 28 days. 36. There are three numbers, 23, 25, and 42; what is the difference between the sum of the squares of the first and last, and the cube of the middlemost? Ans. 13332. 37. Part 1200 acres of land among A, B, and C, so that B may have 100 more than A, and C 64 more than B. Ans. A 312, B 412, C 476. 38. If 3 dozen pair of gloves be equal in value to 2 pieces of holland, 3 pieces of Holland to 7 yards of eatin, 6 yards of satin to 2 pieces of Flanders lace, and 3 pieces of Flanders lace to 81 shillings; how many dozen pair of gloves may be bought for 28s. P Ans. 2 dozen pair. 39. A lets B have a hogshead of sugar of 18 cwt. worth 5 dollars, for 7 do ars the cwt. of which he to pay in cash. B hath paper worth 2 dollars per ream, which he gives A for the rest of his sugar, at 2 dollars per ream; which gained most by the bargain? Ans. A by $19, 20cts. 40. A father left his two sons (the one 11 and the other 16 years old) 10000 dollars. to be divided so that each share, being put to interest at 5 per cent. might amount equal sums when they would be respectively 21 years of age. Required the shares? and 4545 Ans. 5454 dollars. 41. Bought a certain quantity of broadcloth for 399ł 58. and if the number of shillings which it cost per yard were added to the number of yards bought, the sum would be $86; I demand the number of yards bought, and at what price per yard ? Ans. 365 yds. at 21s. per yard. Solved by PROBLEM VI. page 183. 42. Two partners, Peter and John, bought goods to the amount of 1000 dollars; in the purchase of which, Peter paid more than John. and John paid....I know not how much: They then sold their goods for ready money. and thereby gained at the rate of 200 per cent. on the prime cost: they divided the gain between them in proportion to the purchase money that each paid in buying the goods; and Peter says to John, My part of the gain is really a handsome sum of money; I wish I had as many such sums as your part contains dollars, I should then have $960000. I demand each man's particular stock in purchasing the goods. Ans. Peter paid 600 dollars, and John paid 400. THE FOLLOWING QUESTIONS ARE PROPOSED TO 1. Required to lay out a lot of land in form of a long square, containing 3 acres, 2 roods, and 29 rods, that shall take just 100 rods of wall to enclose, or fence it round; pray how many rods in length, and how many wide, inust said lot be? Ans. 31 rods in length, and 19 in breadth. Solved by PROBLEM VI. page 183. 2. A tract of land is to be laid out in form of an equal square, and to be enclosed with a post and rail fence 5 rails high; so that each rod of fence shall contain 10 rails. How large must this noble square be to contain just as many acres as there are rails in the fence that encloses it, so that every rail shall fence an acre? Ans. the tract of land is 20 miles square; and contains 256000 acres. Thus, 1 mile 820 rods: then 320×520÷160=640 acres: and 320×4×10=12800 rails. As 640: 12800 :: 1800: 256000 rails, which will enclose 256000 acres == miles square. APPENDIX, CONTAINING SHORT RULES, FOR CASTING INTEREST AND REBATE 5 TOGETHER WITH SOME USEFUL RULES, 215 FOR FINDING THE CONTENTS OF SUPERFICIES, SOLIDS, &c. SHORT RULES, FOR CASTING INTEREST AT SIX PER CENT. I. To find the interest of any sum of shillings for any number of days less than a month, at 6 per cent. RULE. 1. Multiply the shillings of the principal by the number of days, and that product by 2, and cut off three figures to the right hand, and all above three figures will be the interest in pence. 2. Multiply the figures cut off by 4, still striking off three figures to the right hand, and you will have the farthings, very nearly. EXAMPLES. 1 1. Required the interest of 51. 88. for 25 days. £. 5,8-108×25×2=5,400, and 400×4-1600 Ans. 5d 1,6grs. 2. What is the interest of 911. Ss. for 29 days? Are. 29. Od. 2grs. FEDERAL MONEY. II. To find the interest of any number of cents for any number of days less than a month, at 6 per cent. RULE. Multiply the cents by the number of days, divide the product by 6, and point off two figures to the right, and all the figures at the left hand of the dash, will be the interest in mills, nearly. EXAMPLES. Required the interest of 85 dollars, for 20 days. $ cts. mills. 85=8500 x 20-63283,33 Ans. 283 which is 28 cts. 3 mills. 2. What is the interest of 73 dollars 41 cents, or 7341 cents, for 27 days, at 6 per cent. ? Ans. 330 mills, or 33 cts. HI. When the principal is given in pounds, shillings, &c. New-England currency, to find the interest for any number of days, less than a month, in Federal Money. RULE. Multiply the shillings in the principal by the number of days, and divide the product by 36, the quotient will be the interest in mills, for the given time, nearly, omitting fractions. EXAMPLE. Required the interest, in Federal Money, of 271. 158. far 27 days, at 6 per cent. £ s. Ans, 27 15-555x27+36-416 mills.-41cts. 6m W. When the principai is given in Federal Money, and you want the interest in shillings, pence, &c. NewEngland arrency, for any number of days less than a RULE. Multiply the principal, in cents, by the number of days, and point off five figures to the right hand of the product which will give the interest for the given time, in shil lings and decimals of a shilling, very nearly. EXAMPLES. 8 cts. A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof, in New-England currency? s. d. qrs. Ans. 65,31-6531×25=1;63275=1 7 2 REMARKS. In the above, and likewise in the preceding practical Rules, (page 127) the interest is confined at six per cent. which admits of a variety of short methods of casting; and when the rate of interest is 7 per cent. as established in New-York, &c. you may first cast the interest at 6 per cent. and add thereto one sixth of itself, and the sum will be the interest at 7 per cent. which per haps, many times, will be found more convenient than the general rule of casting interest. S. " EXAMPLE. Required the interest of 75l. for 5 months at 7 per 1 sent. S. 7,5 for 1 month. 5 £. s. d. 37,51 17 6 for 5 months at 6 per cent. Ans. £2 39 for ditto at 7 per cent. A SHORT METHOD FOR FINDING THE REBATE OF ANY Diminish the interest of the given sum for the time by ts own interest, and this gives the Rebate very nearly. EXAMPLES. 1. What is the rebate of 50 dollars for six months, at per cent. ? |