Proof-Add the several shares of gain or loss together, if the work is right, the sum will be equal to the sum of gain, or loss. Examples. 1. A. B. C. and D. joined their stocks, and bought 367 barrels of beef which they sold at $2.75 advance upon the barrel; A.'s stock was 562 dollars; B.'s 646 dollars; C's 394 dollars; and D.'s 600 dollars: I demand the share of each? 367 bar. at $2.75 cents $1009•25 gained. As 2202: 1009 25: 562 : 257·58734 A.'s share. 2203 1009-25 :: 394: 180.58734 C.'s 220.2 2202: 1009 25:: 600: 275:00: D.'s 2. Three men built a ship which cost 4560 dollars of her belonged to A. to B. and the remainder to C. they agreed to freight her with a cargo of lumber worth 1270 dollars, in proportion to their shares; and send her to the W. I. She was lost; I demand the loss of each. Ans. A lost $1457.5: B.lost $2332: C.lost $2040.5 DOUBLE FELLOWSHIP. DEFINITION. Double Fellowship teaches to find the shares of gain, or loss of several persons, who have joined their stocks in trade for unequal times. 1 RULE. Multiply each man's stock by the time it was in trade; then say, as the sum of the products is to the gain or loss, so is the product of each man's stock and time, to his share of the gain or loss. Examples. 1. A. commenced trade with a capital of 500 dollars; in 1 month after, he received B. as a partner, with a capital of 450 dollars; in three month's after this they received C. with a capital of 900 dollars; they traded 4 years from the time that A. commenced business, and gained 3420 dollars; I demand the gain of each? A.'s stock multiplied by the time amt. dols. 84750: 3420 :: 24000: stock. mo. 500×48 24000 A.'s 450X4721150 B's 900X4439600 C's total amount 84750 dols. ct 968-49410 A.'s share. 84750: 3420 :: 21150: 853.48578 B.'s 84750: 3420 :: 39600: 1598-0165250 C.'s 84750 2. A. began trade with a capital of 1300 dollars; he traded 9 months and died: B. offered the fam ily to continue the business, if they would allow his time to be equal to A.'s stock; and divide the gaia accordingly; it was so agreed, and he continued business 1 year and three months from the death of A.; I demand the share of each, allowing the gain to have been 392 dollars. A.'s capital 1300 dollars, and in trade 2 years. B.'s time valued $1300, and in trade, 1 year and The heirs of A. had $241.230700 B. 8150-764800 Ans. 3 months. 39u9 3. B. and D. joined stocks, viz. 500 dollars each; they traded 2 years, and B. took out one fifth of his stock, and they continued their trade 3 years long er, and gained 627 dollars; what is the share of each? Ans. B.'s $293-4844 D.'s $333′5177 PRACTICE. DEFINITION.-Practice is a rule which teaches to solve such questions by division, as are solved by compound multiplication, or single rule of three; it is not so useful in the present currency of the United States as it was in the former currrency ; but in many instances it is still a short and easy way of finding the price of several things. Tables of aliquot parts of a Cwt. & qr: When the price is cents and the quantity whole numbers, RULE. Write down the quantity, as so many dollars, see what parts, the cents in the price, are of a dollar, divide by that part, and the quotient is the answer. Examples. 1. What will 622 yards of India cotton come to, at 25 cts. per yd.? dols. 25 cts,=)622 $155.50 Ans. NOTE. The quantity being written down as so many dols. I considered that 25 cts, were equal to 4 of a dollar, therefore of the quantity is the answer, 2. What is the price of 3472 oranges at 5 cents a piece? Ans. $173.60 CASE II. When the quantity is whole numbers and the price is dols and cents. RULE. Multiply the quantity by the dols. in the price, and work for the cents as in case first. Examples 1. What will 22 thousand of boards come to, at 9 dols. 25 cents per thousand? 25 cts. = 4)22 quantity. 9 198 5:50 $203.50 Ans. 2. What will 20 barr. of cider come to, at 2 dols. 16 cts. per barrel ? CASE III. Ans. $43.20 When the price is no aliquot part of a dollar. RULE.-Divide by two or more numbers, whose sum will make the number required. Examples. 1. What will 622 yards of linnen come to, at 30 cts. per yard? dols. 20 cts. = 622 10 cts. = of 20.124.40 cts. price at 20 cts, 62.20 Ans. $186.60 price at 10 cts. price at 30 cts. 2. What will 642 yards of India cotton come to, at CASE IV. When there are several denominations in the quantity, and the price is dollars and cents. RULE. Multiply the dols. in the price into the whole numbers of the quantity; work for the cents in the price as in the preceding cases; and for the parts in the quantity divide by the aliquot parts of the price of one whole number; add the quotients together the sum is the answer. Examples. 1. What will 112 cwt. 3 qr. 1. bs. of sugar come to, at 12 dols. 25 cts. per cwt.? 25cts.112 cwt. 12 dols. 1344 price at 12 dols. $1372 price of 112 cwt. at $12.95 dols.cts.. 3 qrs.)12.25 14 lbs. of 3 qrs.)9-18+ price of 3 qrs. 1-53 price of 14 lb. 10-71 price of 3 qrs. 14 lb. 1372.00 price 112 cwt. $1382.71 Answer. TARE AND TRET. DEFINITION. Tare and Tret are allowances made the buyer by the seller, for the weight of the box, cask, &c. K |