CASE 2. To know how a commodity must be sold to gain or lose so much per cent. As 100 dollars (or £100) is to the price; so is 100 dollars (or, £100) with the profit added, or loss subtracted, to the gaining or losing price. EXAMPLES. 1. Ir I buy wheat at Doll. 1,25 per bushel, how must I sell it to gain 15 per cent ? OPERATION. As 100: 1,2 5:: 115 115 2. Ir a barrel of rum cost 15 625 125 125 -D.cts.m. 100)1 4,3 7 5(1, 43 7 Ans. 100 437 4 0 0 37 5 300 750 700 5 0 3. Ir 120 lb. of steel cost £7 how must I sell it per lb to gain £15 per cent? Aes. 184 per lb. 2. HAVING the price at which goods are bought and sold, how is the loss, or gain estimated? 3. To know how much a commodity must be valued at to gain or lose so much per cent, what is the method of procedure? 4. How may questions in Loss and Gain be proved ? EXERCISES. 1. A DRAPER bought 100 yards of broadcloth for .56. I demand how he must sell it per yard, to gain 15 in laying out £100 ? Ans. 12s. 10d. 2q. 180 20 2. BOUGHT 30 hogsheads of molasses, at 600 dollars; paid in duties Dolls. 20,66; for freight Dolls. 40,78; for porterage Dolls. 6,05 and for insurance, Dolls. 30,84: If I sell it at 26 dollars per hogshead, how much shall I gain per cent? Ans. Dolls. 11, 695. THIS rule is particularly useful to Workmen and Artificers in casting up the contents of their work. DIMENSIONS are taken in feet, inches and parts. Inches and parts are sometimes called primes ('), seconds (''), thirds (''), and fourths (""). TABLE 12 Fourths make 1 Third, 12 Thirds 12 Seconds - - 1 Second. By this rule also may be calculated the solid contents of bodies, having the meas ures of their different sides, and is 1 Inch,or Prime. useful, therefore, in measuring wood, 12 Inches, or Pr.1 Foot. RULE. very 1. UNDER the multiplicand write the corresponding denominations of the multiplier. 2. MULTIPLY each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write the result of each under its respective term, observing, to carry an unit for every 12, from each lower denomination to its superior. 3. In the same manner multiply the multiplicand by the inches in the mul tiplier, and write the result of each term in the multiplicand thus multiplied, one place to the right hand in the product. 4. PROCEED in the same manner with the other parts in the multiplier, which if seconds, write the result two places to the right hand; if thirds, three places, &c. and their sum will be the answer required. THE more easily to comprehend the rule, NOTE. Feet multiplied by Feet EXAMPLES. give Feet...Feet multiplied by Inches give Inches...Feet multiplied by Seconds give Seconds... Inches multiplied by Inches give Seconds...Inches multiplied by Seconds give Thirds...Sec. 1. MULTIPLY 7 feet, 3 inches, 2 sec- onds multiplied by Seconds give Fourths. onds, by 1 foot, 7 inches, and 3 seconds. OPERATION. F. I. 1 74 37 23 3 2 2.10 4 HERE I multiply the 7f. 3in. 2" by the lf. in the multiplier, which gives seconds, inches, and feet. NEXT I multiply the same 7f. 3in. 2". by the 7in. saying 7 times 2 is 14 which is once 12 and 2 over, which (2) I set down one place to the right hand, that is in the place of thirds, and carry 1 to the next place, & proceed in the same manner with the other terms. Lastly I multiply the multiplicand by the 3" saying 3 times 2 is 6 which I set down two places to the right hand and so proceed with the other terms of the multiplicand. The sum of all the products is the answer. 7. How much wood in a load, which measures 10f. in length, 3ƒ 9in. in width, and 4f. 8in in height; and how much will it cost, at 1 dol. 33 cts. per cord? Ans. 1 cord, and 47 solid feet over; it will cost 1 doll. 81 cts. 8m. § 8. Duodecimals ; OR, CROSS MULTIPLICATION. THIS rule is particularly useful to Workmen and Artificers in casting up the contents of their work. DIMENSIONS are taken in feet, inches and parts. Inches and parts are sometimes called primes ('), seconds (''), thirds ('''), and fourths (''''). TABLE 12 Fourths make 1 Third, 1 Second. By this rule also may be calculated the solid contents of bodies, having the meas ures of their different sides, and is very 1 Inch,or Prime. useful, therefore, in measuring wood. 12 Inches, or Pr.1 Foot. 12 Thirds 12 Seconds RULE. 1. UNDER the multiplicand write the corresponding denominations of the multiplier. 2. MULTIPLY each term in the multiplicand, beginning at the lowest, by the feet in the multiplier, and write the result of each under its respective term, observing, to carry an unit for every 12, from each lower denomination to its superior. 3. In the same manner multiply the multiplicand by the inches in the mul tiplier, and write the result of each term in the multiplicand thus multiplied, one place to the right hand in the product. 4. PROCEED in the same manner with the other parts in the multiplier, which if seconds, write the result two places to the right hand; if thirds, three places, &c. and their sum will be the answer required. THE more easily to comprehend the rule, NOTE. Feet multiplied by Feet EXAMPLES. give Feet...Feet multiplied by Inches give Inches... Feet multiplied by Sec onds give Seconds...Inches multiplied by Inches give Seconds...Inches multiplied by Seconds give Thirds...Sec 1. MULTIPLY 7 feet, 3 inches, 2 sec- onds multiplied by Seconds give Fourths. onds, by 1 foot, 7 inches, and 3 seconds. 17 3 4 2 10 2 1 9 9 6 HERE I multiply the 7f. 3in. 2" by the lf. in the multiplier, which gives seconds, inches, and feet. NEXT I multiply the same 7f. 3in. 2". by the 7in. saying 7 times 2 is 14 which is once 12 and 2 over, which (2) I set down one place to the right hand, that is in the place of thirds, and carry 1 to the next place, & proceed in the same manner with the other terms. Lastly I multiis 6 which I set down two places to the right hand and so proceed with the ply the multiplicand by the 3" saying 3 times 2 other terms of the multiplicand. The sum of all the products is the answer. |