ries of equations, in which all the members are given, except the 2d member of the 1st equation; .. if the continued product of the 1st members be divided by the continued product of the known 2d members, the quotient must necessarily be the unknown 2d member, which is the number sought. Ex. 3. If 5 gal. molasses are equal in value to 2 bush. corn, and 18 bush. corn to 3 cords of wood, how many gallons of molasses are equal in value to 7 cords of wood? All similar examples may be solved in like manner. To solve questions in Conjoined Proportion, = Hence, RULE. Write the demanding term, and at the right of it a blank in the place of the term sought, with the sign between them; write the term of the same name as the demanding term under the blank, and that which is equal to it in value at the left of it, with the sign between them; and thus proceed, writing the term of the same name as the one last placed, on the right and the term equal to this on the left, till all the terms are written ; then the continued product of the left-hand members, divided by the continued product of the right-hand members, will be the term sought. Ex. 4. If 9£ sterling money equals 12£ N. E. currency, 6£ N. E. equals 8£ N. Y.,*16£ N. Y. equals 15£ N. J. and 45£ N. J. equals 28£ Ga. currency, how many pounds sterling are equal in value to 56£ Ga. currency? Ans. 54. 5. If 20 acres of land in Andover are worth as much as 30 acres in Boxford, 50 in Boxford as much as 45 in Methuen, 25 in Methuen as 20 in Lawrence, and 33 in Lawrence as 40 in Bradford, how many in Andover are equal in value to 1800 in Bradford? 6. If 20 boys will perform as much labor as 15 men, and 12 men as much as 18 women, how many boys would be required to perform as much labor as 27 women ? 7. If 483 American eagles are equal in value to 1000 English sovereigns, 150 English sovereigns to 161 French Louis d'ors, 22 Louis d'ors to 45 Italian sequins, 95 sequins to 44 German Carolins, and 88 Carolins to 190 Swiss ducats, how many American eagles are equal in value to 50 Swiss ducats? Ans. 11. 264. All these examples may be solved by a series of simple proportions, and, of course, by compound proportion. Each example may also be analyzed in various different ways. For illustration, let us take Ex. 3: – If 5gal. molasses are equal in value to 2bush. corn, and 18bush. corn to 3cords of wood, how many gallons of molasses are equal in value to 7cords of wood? § 29. PROFIT AND LOSS. 265. “PROFIT AND LOSS," as a commercial term, signifies the gain or loss in business transactions. The rule may refer to the absolute gain or loss, or to the percentage of gain or loss on the purchase price of the property considered. 266. PROB. 1.-To find the absolute gain or loss on a quantity of goods sold at retail, the purchase price of the whole quantity being given, RULE.-Ascertain the whole sum received for the goods, and the difference between this and the purchase price will be the gain or loss. Ex. 1. Bought 16bbl. of flour for $100 and sold it at $7 per bbl.; did I gain or lose? how much total and per bbl.? Ans. Gained $12 total; 75c. per bbl. 2. Bought 75yds. broadcloth for $250 and sold it at $4 per yd.; did I gain or lose? how much total and per yd.? Ans. 3. Bought 13cwt. 1qr. 19lb. of sugar for $107.52 and sold it at 64cts. per lb.; did I gain or lose? how much total and per lb.? Ans. Lost $23.52 total; 13c. per lb. 4. Bought 164 yards of broadcloth and as many yards of cassimere for $1107; sold the broadcloth at $3 per yd. and the cassimere at as much per yd. Did I make or lose? how much? 267. PROB. 2.-To find the percentage of gain or loss. RULE 1.—Find the total gain or loss by Art. 266, and then say, as the purchase price is to the total gain or loss, so is 100 per cent. to the gain or loss per cent. NOTE.-The par value of an article is its first cost. Ex. 1. What do I gain per cent. if I buy flour at $6 and sell it at $7 per bbl. Cost: Gain : : Par Value : Gain per cent. :: 163 per cent., Ans. 2. Bought a share of the Boston & Maine Railroad stock for $108 and sold it for $105? what was my loss per cent.? $108: $3 :: 100: 27, Ans. (a) RULE 2.-Make a common fraction, writing the gain or loss for the numerator and the cost of the article for the denominator, and then reduce the fraction to a decimal. Thus, in Ex. 2, $3 is the loss and $108 the cost,.. the loss is T3 of the purchase money and 188 T88.027, Ans. = = 8 .023; i. e. 23 hundredths or 27 per cent. of the cost. 3. Purchased a quantity of merchandise for $3496 and sold the same for $3670.80; what did I gain per cent.? Ans. 5 per cent. 1979 4. Bought a quantity of goods for $3496 and sold the same to John Smith on his note at 60 days for $3709.75 -47% This note was, on the same day, discounted at the Andover Bank. Did I make or lose? how much per cent.? Ans. Gained 5 per cent. 5. Bought a flock of sheep at $4 per head and sold them at $5; what per cent. was gained? 6. Bought sheep at $5 per head and sold them at $4; what per cent. was lost? 7. Bought goods for $4000, and, in one year, sold the same for $4310, out of which paid $190 for storage, etc.; how much per cent. on the first cost was lost? 268. PROB. 3.- The purchase price of an article being given to find such a selling price as to gain or lose a certain per cent. on the cost, RULE 1.-Multiply the purchase price by the per cent. to be gained or lost, written decimally, and add the product to or subtract it from the purchase price. Ex. 1. Bought goods for $400; how must the same be sold so as to gain 25 per cent.? 2. Bought a horse for $150, but it being injured, I am willing to lose 10 per cent.; for what may I sell him? (a) RULE 2. As 100 is to 100 increased by the per cent. to be gained or diminished by the per cent. to be lost, so is the purchase price to the selling price. By this rule the 1st example will be solved thus : — Par value Premium value :: 1st Cost: Selling price. 100 per cent.: 125 per cent. :: The 2d example is solved thus: $400 $500, Ans. Ex. 3. Bought pepper at 12 cts. per lb. ; how shall it be sold to lose 10 per cent.? Ans. 11c and 21⁄2m. 4. Bought 3 cwt. of sugar at 12 cts.; how shall the same be sold per lb. so as to gain 20 per cent. ? 5. Bought 6 shares of Exchange Bank Stock at $100 per share; how shall the same be sold to gain 62 per cent. ? 269. PROB. 4. To find the first cost of an article when we know the selling price and the gain or loss per cent. on the cost, RULE. Say as 100 increased by the per cent. to be gained or |