DEM. It is evident, that the operation here, is as in the Rule of Three Direct, and that each man's share of the gain, is in proportion to his stock. $1800 $1400 Same example by Division and Multiplication. 3200)800,00 (,25 cents on a dollar.,25 2. A, B, and C, companied; A, put in 400, B, 600, C, 800 dollars; they gained 540 dollars; what must each have of the gain? Ans. A's share 120, B's 180, C's $240. 3. Divide 742 dollars between A, B, and C, so that B, shall have twice as much as A, and C, twice as much as B; what will be the share of each? Ans. A's 106, B's 212, C's $424. 4. A captain, mate, and 20 seamen took a prize worth 4674 dollars; of which the captain is to have 12 shares, and the mate 6 shares; the remainder is to be divided equally among the seamen; how much is each person's share? Ans. The captain's share is $1476, the mate's {$738, quch seaman's share $123. Questions on Single Fellowship. What is Single Fellowship? A. The Rule of Three Direct applied to the business of partners in trade, to ascertain each man's share of the gain or loss. Why does this belong to the Rule of Three? A. Because it is evident that each man's share of gain or portion of loss, must be in proportion to his stock. Can Fellowship be worked by Multiplication and Division? A. It can, by dividing the whole gain by the whole stock; the quotient will be the gain on a dollar, and that repeated by each man's stock, will give the gain of each. DOUBLE FELLOWSHIP. In Double Fellowship, or Fellowship with time, the stocks are continued in Trad unequal times. This rule as well as Single Fellowship, belongs strictly to the Rule of Three Direct. RULE.-Multiply each man's stock by the time it was continued in trade; then, as the whole sum of the products, is to the whole gain, or loss, so is each man's product, to his share of the gain or loss. EXAMPLES. 1. Three persons traded in company; A, put in 400 dollars for 2 years, B, 400 dollars for 4 years, and C, 200 dol have of the gain? A$400X2 lars for 8 years; they gained 600 dollars; what must each Ans. 8001 800 $120 A's sh. B 400X4=1600 1600: 240 B's sh. As 4000: 600 :: C 200X8 1600 1600: 240 C's sh. Proof, $600 DEM. From the example given, it is evident that this is strictly the Rule of Three Direct, and each person's share of gain or loss, must be in proportion to his product of money and time. A's share of gain is only one half as much as B's, because his money is invested in trade only half as long; and C's is equal to B's, because he has half as much money as B, invested in trade double the time; and it is plain, that 200 dollars must gain as much in 8 years as 400 dollars in 4 years.This can be reduced back to Multiplication and Division, by dividing the whole gain, 600 dollars, by the sum of the products; the quotient, which would be the gain on a dollar, must then be multiplied separately by each man's product for the gain of each. 2. Two partners gained by trading, 800 dollars; A's stock was 1200 dollars for 8 months, and B's $800 for 10 months; what is each partner's share of the gain?· Ans. A's share $436,36cts. 3m., B's $363,63cts. 6mo. 3. A, B, and C, entered into partnership; A, put in $400 for 6m.; B, $250 for 8mo.; C, $360 for 51mo.; on adjusting their accounts they find their loss to be $638; what is each man's loss? Ans. A's loss $240, B's $200, C's $198. QUESTIONS ON DOUBLE FELLOWSHIP. Wherein does Double Fellowship differ from Single Fellowship?— A. In Double Fellowship, the stocks are contined in trade unequal times, which is not the case in Single Fellowship. Does Double Fellowship depend on the Rule of Three Direct the same as Single Fellowship? A. Just the same, and may be reduced back to division and multiplication. How is the work prepared for a statement, in the Rule of Three? A. By multiplying each man's stock by the time it was continued in trade, and then adding the several products; then say, as the sum of the products, is to the whole gain or loss, so is each man's product, to his share of the gain or loss. BARTER, Is exchanging one commodity for another, according to the price or value agreed upon by the parties concerned. It is merely an application of the Rule of Three Direct to the exchange of specifick articles, so that neither party shall sustain a loss. The operation is frequently easier performed by multiplication and division. RULE. Find the value of the commodity,whose quantity is given, then find what quantity of the other, at the proposed rate, can be purchased for the same money, and it will give the answer. EXAMPLES. 1. How much corn, at 40cts. a bushel, must be given for 60 bushels of wheat, at 80cts. a bushel? Ans. 120 bushels. By Multiplication and Division. bu. cts. bu. 1:,80::60 60 cts. DEM.-It is plain, when we repeat the price of 1 bushel of wheat, by the num ,40)48,00(120. Ans. ,40)48,00(120 A. ber of bushels, that 40 80 80 0 the product is the 40 80 price of the whole quantity; then, when we divide the 80 0 whole cost of the wheat, by the price of 1 bushel of corn, the quotient must be the quan tity of corn; because as often as the sum of 40 cents is contained in the whole money, so often a bushel of corn can be had in exchange for the wheat. 2. What quantity of butter, at 10 cents a pound, must a lady give in barter for 8 yards of satin, at 1 dollar 25 cents per yard? Ans 100 pounds. When the quantities of both commodities are given, and the difference of their values is to be paid in money; and the value of both, and the difference of their values, will be the answer. When one commodity is rated above cash price, to find the bartering price of the other, say, as the cash price of the one, is to its bartering price, so is the cash price of the other, to its bartering price. 3. A, lets B, have 50 bushels of rye, at 45 cents a bushel, for which he receives 60 bushels of oats, at 25 cents a bushel, and the balance in money, how much money must A receive? Ans. $7,50 cents. 4. A, has calico worth 18cts. a yd., ready money, but in barter he will have 25 cents; B, has broadcloth worth $3,75cts. per yard, ready money; at what price ought the broadcloth to be rated in barter? Ans. $5,20 cents 8 mills. QUESTIONS ON BARTER. What is harter? A. It is strictly the Rule of Three Direct applied to the exchange of one commodity for another so that neither party shall sustain loss. When you have the price of one quantity or commodity, how do you find the quantity of the other commodity, which may be received for the money? A. Divide the money by the price of a unit of the required quantity. When the price and quantity of both commodities are given, how do you find the balance which is to be paid in money? A. Subtract what one commodity comes to, from the amount of the other. When the ready money price of one commodity, is less than its bartering price, how do you find the bartering price of the other commodity? A. As the ready money price of the one, is to its bartering price, so is the ready money price of the other, to its bartering price. LOSS AND GAIN, Is only a particular application of the Rule of Three Direct, by which merchants and traders discover their profits, or loss per cent, or by the gross: It also teaches them to raise or fall on the price of their goods, so as to gain or lose so much per cent, &c. CASE I-To know what is gained or lost per cent. RULE. First see what the gain or loss is, by subtraction; then, as the price it cost, is to the gain or loss, so is $100, or £100, to the gain or loss per cent. EXAMPLES. 1. If a merchant buy calico, at 24 cents a yard, and sell it, at 36cts per yard; what does he gain per cent, or what does he gain in laying out $100? Ans. $50, or 50 per cent. cts. cts. $ ,24:,12:: 100,00 cts. ,36 DEM.It is evident, that the merchant on the sale of one yard gained half what it cost him, consequently he must have gained $50, in laying out $100; because the gain on 100 dollars must be in the same proportion as the gain on twenty four cents. 2. Bought butter at 9cts. a pound, and sold it at 12cts. a pound; what was gained per cent ? Ans. 33 per cent. 3. Bought 30 yards of broadcloth at $4,50 cents per yard, and sold it for 110 dollars; what was gained or lost per cent? Ans. $18,51cts. 8m. loss per cent. CASE II. To know how a commodity must be sold, to gain or lose so much per cent. RULE.-As $100, or £100, is to the price it cost, so is $100 or £100, with the profit added, or the loss subtracted, to the gaining or losing price. EXAMPLES. 1. If a merchant buy sugar, at 9cts. a pound, how must he sell it per pound, to gain 25 per cent? Ans. 11cts. 2m. DEM.-As the third term is increased by the per cent above the first, so the fourth term or answer, must increase above the second term. To gain 25 per cent, is adding one fourth the given 2. If a man buy corn, at 40 cents per bushel, how must he sell it, to gain 30 per cent? Ans. 52 cents per bushel. CASE III-When there is gain or loss per cent, to know what the commodity cost. RULE.-As $100, or £100, with the gain per cent added, or the loss per ct. subtracted, is to the price, so is 100 dollars, or 100 pounds, to the first cost. EXAMPLES. 1. If a yard of cloth be sold at $4,50cts., and there is gained $25,50cts. per cent, what did the yard cost? Ans. $3,58 cents 5 mills. 125,50 : 4,50 :: 100,00 : Ans. $3,58cts. 5m. 2. By selling wheat, at 75 cents per bushel, I lose at the rate of 30 per cent, what was the first cost of the wheat per bushel? Ans. $1,07 cents. CASE IV.-If by wares sold, at a given rate, there is so much gained or lost per cent, to know what would be gained or lost per cent, if sold at another rate. RULE. As the first price is to $100 or £100, with the profit per cent added, or the loss per cent subtracted, so is the other price, to the gain or loss per cent, at the other price. NOTE.-If the answer exceed 100, the excess is gain per cent, but if it be less than 100, the deficiency is loss per cent. EXAMPLES. 1. If brandy, sold at $1,12 cents per gallon, be 20 per cent profit, what gain or loss per cent shall I have, if I sell the same at 95cts per gallon? Ans. Gain $1,78,5m. pr. ct. $1,12 120 :: 95: 101,78,5 |