2 Bought 30 bushels of wheat; the first bushel for 2d. the second 4d. the third 8d. doubling the price of each preceding bushel for that of the next; query the amount, and price per bushel at an average? answer 298261 12s 4d. per Bushel. 3 Sold 15 yards of sattin, the first yard for 1s. the second for 2s. the third for 4s. &c. what sum did they amount to? answer 16381 7s. 4 Admit a goldsmith sold one lb. of gold, at one farthing for the first ounce, a penny for the second, 4d. for the third, &c. in a quadruple proportion; what did it amount to ? and what did he gain by it, supposing it cost him 4l. per ounce ? 5 What sum would purchase a horse with 4 shoes, and 8 nails in each shoe, at one farthing for the first nail, a half-penny for the second, a penny for the third, &c. doubling to the last? answer 44739241 5s 3d.3 6 Suppose a man wrought 20 days, and received for the first day 4 barley corns, for the second 12, for the third 36, &c. in a triple proportion; what did the twenty days labour come to, rating the barley at 2s. 6d. per bushel ? answer 17731 7s 6d. Note. 7680 Wheat, or Barley corns, are supposed to make a pint. 7 Sold 30 yards of velvet, at 2 pins for the first yard, 6 for the second, 18 for the third, &c. and these disposed of at one farthing per 100, how much did the velvet amount to? And whether did the seller gain or lose, and how much, supposing-the prime cost of the velvet at 50%. per yard? answer { 21446992927 13s Od Amount. 2144697792/ 138 Od Gained. 8 A certain person married his daughter on new year's day, and gave her one guinea towards her portion, promising to double it on the first day of every month for one year; what was her portion in sterling money? answer 4299/ 15s. SIMPLE SIMPLE INTEREST-BY DECIMALS. Note. The ratio is the Interest of 11. for one year, and is thus found. :{ £.£. 100 : 5 :: 1,05 As 100: 5,5 : 1,055 100 : 6 :: 1,06 &c. Which is only dividing the rate per cent. by 100, by moving the point two places to the left. The principal, time, and ratio given, to find the interest, and amount. RULE. Multiply the principal, time, and ratio together, the last product will be the interest, commission, brokage, &c. to which add the principal, and the sum will be the amount. Note. In operations of interest by decimals, the money should be in the denominations of pounds, or dollars, and the time in years, with their parts (if any) annexed decimally. EXAMPLES. 1 Required the amount of 5371 10s. at 6 annum for 5 years? Principal 537,5×5×,06=161,25 Interest. 537,5 Principal. £. 698,75=6981 15s. answer. 2 What is the interest of 9177 16s. at 5 per cent. per annum for 7 years 8 ? answer 211 4s 7d. 3 If my correspondent be to have 43 per cent. what will his commission on 391 17s. come to? answer 171 12s 7d. 4 What will be the interest and amount of 5677 10s, in 9 years, at 6 per cent. per annum ? 3061 9s. Interest. answer 2873 19s. Amount. 5 What is the interest of 47261 18s 6d. for 34 years, at 7 per cent. per annum ? answer 1158l is 1ld. 6 What will 9526l 12s 9d. amount to in 12 years and 9 months, at 7 per cent. per annum ? answer 180291 3s 2d.ş A ALLIGATION. LLIGATION is a rule for adjusting the prices and When several simple quantities and their prices are given, and a mean price of any part of the compound is required. RULE. As the sum of the several quantities Is to their total value; So is any part of the composition To its value. EXAMPLES. 1 If 19 bushels of wheat at 6s. the bushel, 40 of rye at 4s. and 12 of barley at 8s. be mixt together; what is a bushel of this mixture worth? )310(4 44 answer. 2 A grocer mixed sugars; 2C.wt. at 56s. 1C.wt. at 43s. and 2C.wt. at 50s. per C.wt. what is 3C.wt. of this mixture worth P answer 71 13s. 3 If 3 If 4oz. of silver, worth 5s. the ounce, be melted with 8oz. at 4s. what is one ounce of this mixture worth? answer 4s 4d. 4 A wine merchant mixes 12 gallons of wine at 4s 10d. the gallon, with 24 gallons, at 5s 6d. and 16 at 6s 3d.1; what is a gallon of this mixture worth ? answer 5s. 7d. 5 A goldsmith melted together 8oz. of gold of 22 carats fine, 1lb. 8oz. of 21 carats fine, and 10oz. of 18 carats fine; what is the quality or fineness of the composition ? answer 20 carats fine. 6 A refiner melted 5lb. of silver bullion of 8oz. fine, with 10lb. of 7oz. and 15lb. of 6oz. fine; of what fineness is 1lb. of this mass? answer 60z. 13dwt. 8gr. fine. CASE 2. When the prices of several simples are given, to find how much of each, at their respective rates, must be taken to make a compound at any proposed price; RULE. Write the rates of the simples under each other; link each rate, which is less than the mean rate, with one or more that is greater; the difference or sum of the differences, between each rate and the mean price, placed opposite the respective rate or rates, with which it is linked, will be the several quantities required. Note 1. If all the given prices be greater, or less than the mean rate, they must be linked to a cipher. 2. Different modes of linking will produce different answers. EXAMPLES. 1 How much rye at 4s. the bushel, barley at 3s. and oats at 2s. will make a mixture worth 2s 6d. the bushel? 48. Mean rate 20 36 { 24 6 at 4 6 at 3 18+6=24' 2 answer. 2 Canary at 2s. a quart, Sherry at 16d. and Malaga at 1s. how much of each must be taken, that the mixture may be worth is 6d. the quart? answer 6 8 quarts of Canary, Sherry, and Malaga. 3 A druggist had several sorts of tea, viz. at 12s. per lb. at 11s. at 9s. and at 8s. how much of each sort must be taken to be sold at 10s. per lb. lb. s.p.lb. (2 at 12 lb. s.p.lb. lb. s.p.lb. 4 How much sugar at 4d. at 6d. and at 11d. per pound, must be mixed together, so that the composition may be worth 7d. per lb. answer 1lb. or 1 C.wt. of each, or any other weight of equal quantity. may be 5 It is required to mix several sorts of wine, at 3s. 5s. and 7s. per gallon, with water, that the mixture worth 4s. per gallon; how much of each sort must the mixture consist of? answer 1 gal. wine at 3s. 1 ditto. at 5s. 4 ditto at 7s. and 3 gals. water. CASE 3. When the rate of all the simples, the quantity of one of them, and the compound rate of the whole mixture are given, to find the several quantities of the rest; RULE. Place the mean rate, and the several prices, and take their differences, as in case 2; then, As the differences of the same name with the quantity given Is to the rest of the differences respectively; To the several quantities required. 02 EXAME |