Ans. 1 1 1 2 What part of 25 is of a unit? 33. If A can do a piece of work alone in 10 days, B in 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 à, in the third i, 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. 282 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 pairs of gloves be equal in value to 2 pieces of Holland, 3 pieces of Holland to 7 yards of satin, 6 yaris of satin to 2 pieces of Flanders lace, and 3 pieces of Flanders lace to 81 shillings; how manv dozen pairs of gloves may be bought for 28s. ? Ans. 2 dozen pairs. 39. A lets B have a hogshead of sugar of 18 cwt., worth 5 dollars, for 7 dollars the cwt. į of which he is to pay in cash. B hath paper worth 2 dollars per ream, which he gives A for the rest of his sugar, at 21 dollars per ream; which gained most by the bargain ? Ans. A by $19 20 cts, 40. A father left his two sons (the one 11 and the other 16 years old) 10,000 dollars, to be divided so that each share being put to interest at 5 per cent. might amount to equal sums when they would be respectively 21 years of age. Required the shares ? Ans. 5454, 1 and 4545, dollars. 41. Bought a certain quantity of broadcloth for 3831. 58. and if the number of shillings which it cost per yard were added to the number of yards bought, the sum would be 386; I demand the number of yards bought, and at what price per yard? Ans. 365 yds. at 21s. per yard. 171. 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 $960,000, I demand each man's particular stock in purchasing the goods. Ans. Peter paid $600 and John paid $400. THE FOLLOWING QUESTIONS ARE PROPOSED TO SURVEYORS: 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 sound; pray how many rods in length, and how many wide, must said lot be? Ans. 31 rods in length, and 19 in breadth. Solved by PROBLEM VI. page 171. 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 256,000 acres. Thus, 1 mile=320 rods: then 320 x 320-160=640. acres : and 320 x 4x10=12,800 rails. As 640 : 12,800 :: 12,800 : 256,000, rails, which will enclose 256,000 acres R0 miles squiare. AN APPENDIX, CONTAINING SHORT RULES, FOR CASTING INTEREST AND REBATE; TOGETHER WITH SOME USEFUL RULES, MY FINDING THE CONTENTS OF SUPERFICES, SOLIDS, &c. SHORT RULES, IOR CASTING INTEREST AT SIX PER CENT. 1, '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 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. in pence. EXAMPLES . 1. Required the interest of 5l. 8s. for 25 days. Ans. 5d. 1,6qrs. 2. What is the interest of 211. 3s. for 29 days? Ans. 2s. Od. 2 grs. 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 pro duct 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 20:6=283,33 Ans. 283 which is 28 cts. 3 mills. 2. What is the interest of 73 dollars 41 cents, or 7311 cents, for 27 days, at 6 per cent. ? Ans. 330 mills, or 33 cts. III. When the principal is given in pounds, shillings, &c New-England currency, to find the interest for any num. ber 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 tho interest in mills, for the given time, nearly, omitting fractions. EXAMPLE. Required the interest in Federal Money, of 271. 15s. for 27 days, at 6 per cent. £. Ans. 27 15=555 X 27-36=416 mills.=41 cts. Om. IV. When the principal is given in Federal Money, and you want the interest in shillings, pence, &c. New-Eng. land currenty, for any number of days less than a month 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 shillings and decimals of a shilling, very nearly. EXAMPLES. S. A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof in New-England currency? $ cts. 8. d. qi's. Ans. 65,31=6531 X 25=1,63275=1 7 2 REMARKS.- In the above, and likewise in the preceding practical Rules, (page 115) the interest is confined at 6 per cent. which admits of a variety of short methods of casting: and when the rate of interest is 7 per cent. as estilblished in New-York, &c. you may first cast the interest at i per cent. and add thereto one sixth of itself, and the sun vill be the interest at 7 per ct., which perhaps, many times vill be found more convenient than the general rule of cast ing interest. EXAMPLE. Required the interest of 75l. for 5 months, at 7 per cent 7,5 for 1 month. £. s. d. A SHORT METHOD FOR FINDING THE REBATE OF ANY GIVEN SUM, FOR MONTHS AND DAYS. RULE.Diminish the interest of the given sum for the time by its own interest, and this gives the Rebate very ncarly. EXAMPLES. 1. What is the rebate of 50 dollars, for 6 months, at 6 per cent. ? |