5s. 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. 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 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 round; 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 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 rail shall fence an acre? every Ans. the tract of land is 20 miles square, contains 256000 acres. and Thus, 1 mile-320 rods: then 320X320-160=640 acres and 320×4×10=12800 rails. As 640: 12800 :: 12800: 256000 rails, which will enclose 256000 acres= 6 miles square. 215 AN APPENDIX, CONTAINING SHORT RULES, FOR CASTING INTEREST AND REBATE; TOGETHER WITH SOME USEFUL RULES, FOR FINDING THE CONTENTS OF SUPERFICIES, SOLIDS &c. SHORT RULES, FOR 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 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. Required the interest of 51. 8s. for 25 days. 5,8=108X25X2=5,400, and 400x4=1,600 2. What is the interest of 211. 3s. for 29 days? ARs. 2s. Od. 2qrs. 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. S. cts. 85-8500×20÷6=283,33 mills. Ans. 288 which is 28 cts. 3 mills. 2. What is the interest of 75 dollars 41 cents, or 7341 cents, for 27 days, at 6 per cent.? 米糖 Ans. $50 mills, or SS cts. III. 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. 15s. for 27 days, at 6 per cent. £• S. S. Ans. 27 15=555×27÷36–416 mills.=41cts. 6m. IV. When the principai is given in Federal Money, and you want the interest in shillings, pence, &c. NewEngland currency, 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 shilings and decimals of a shilling, very nearly. EXAMPLES. A note for 65 dollars, 31 cents, has been on interest 25 days; how much is the interest thereof, in New-England currency p $cts. $. qrs. s. d. 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 perhaps, many times, will be found more convenient than the general rule of casting interest. EXAMPLE. Required the interest of 756. for 5 months at 7 per cent. S. 7,5 for 1 month. 5 £. s. d. 37,5-1 17 6 for 5 months at 6 per cent. 6 3 Ans. £2 39 för ditto at 7 per cent. 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 nearly. EXAMPLES. 1. What is the rebate of 50 dollars for six months, at 6 per cent. ? The interest of 50 dollars for 6 months, is $ cts. 1 50 4. Ans. Rebate, $1 46 2. What is the rebate of 150l. for 7 months, at 5 per cent. ? s. d. terest of 150l. for 7 months, is 4 7 6 mterest of 4l. 7s. 6d. for 7 months, is 2 61 Ans. £4 4 11 nearly. By the above Rule, those who use interest tables in their counting-houses, have only to deduct the interest of the interest, and the remainder is the discount. A concise Rule to reduce the currencies of the different States, where a dollar is an even number of shillings, to Federal Money. RULE I. Bring the given sum into a decimal expression by inspection, (as in Problem I. page 87) then divide the whole by,3 in New-England and by,4 in New-York currency, and the quotient will be dollars, cents, &c. EXAMPLES. 1. Reduce 54l. 8s. 31d. New-England currency, to Federal Money. 8)54,415 decimally expressed. Ans. $181,38 cts. 2. Reduce 7s. 114d. New-England currency, to Fedepal Money. 7s. 11 d. 0,399 then, ,3),399 Ans. $1,33 3. Reduce 513l. 168. 10d. New-York, &c. currency, to Federal Money. ,4)513,842 decimal Ans. $1284,00 |