17. A regiment of soldiers, confifting of 745 men, is to be clothed, each fuit to contain 3 yards of cloth, which is 1 yard wide, and lined with shalloon yard wide; how many yards of shalloon will line them ? As 745×3: I :: : 4097 yds. Ans. 18. If a fuit of clothes can be made of 4 yards of cloth, 1 yard wide; how many yards of coating, of a yard wide, will it require for the fame person ? yd. yds. yd. yds. gr. n. As 1 : 4 :: : 61 34 Answer. ABBREVIATIONS. To know whether a fraction, when abbreviated, be equivalent in all respects to the original given fraction. RULE.-As the numerator of the fraction, in its lowest terms, is to its denominator; so will the nume. rator of the original fraction be to its own denomi nator. Or, as one numerator is to the other; fo will one denominator be to the other, &c. A owes B £75 13s. 6d. now £100 of A's money is equal to 140 of B's; what must A pay to fatisfy the faid debt? As 5:7:: 100: 140-Or, as 5: 100 :: 7: 140. COMPOUND COMPOUND PROPORTION, OR, DOUBLE RULE OF THREE, Teaches to refolve such questions as require two, or more statings, by fimple proportion; and that, whether direct, or inverse :- It is composed (commonly) of 5 numbers to find a fixth, which, if the proportion be direct, must bear such proportion to the 4th and 5th, as the 3d bears to the 1st and 2d: But if inverse, the 6th number must bear such proportion to the 4th and 5th, as the Ist bears to the 2d and 3d. Always place the three conditional terms in this order: That number, which is the principal cause of gain, lofs or action, possesses the first place; that which denotes the space of time or distance of place, the fecond; and that, which is the gain, loss or action, the third; this being done, place the other two terms, which move the question, under those of the same name, and if the blank place, or term fought, fall under the third place, then the question is in direct proportion; therefore, RULE 1. Multiply the three last terms together, for a dividend, and the two first for a divisor: But if the blank fall under the first or second place; then, the proportion is inverse; therefore, RULE 2. Multiply the first, second and last terms together for a dividend, and the other two for a divifor, and the quotient will be the answer. I. If £ 100 gain £6 in a year; what will £400 gain in 9 months? £. P. Mo.f. Int. 100: 12 :: 6 Terms in the supposition, or conditional terms. Terms which move the question. 400: 9 Here, the blank falling under the third place, the question is in direct proportion, and the answer must be found by the first rule; therefore, 400×9×6=21600 For the dividend, and See the work at large. 12,00)216,00(18). Answer. £. Pr. Mo. £. Int. 100: 12 :: 6 400: 9 9 2. If £ 100 will gain £6 in a year; in what time will £400 gain £18? 100: 12 :: 6 Terms in the supposition. 400: :: 18 Terms which move the question. Here, the blank falling under the 2d place, the queftion is in reciprocal or inverse Proportion, and the answer must be fought by the fecond Rule: Therefore, 100 × 12 × 18=21600 For the dividend. 3. If £400. gain £18 in 9 months; what is the rate per cent. per annum ? Pr. 228+215 10s. +187 105.631. and 631÷2=315 105. the whole gain; then, £315 105.-228=£87 10. C's gain, £315 105. -1215 105.6100 A's gain, and £315 105.-£187 10s. = £ 128 B's gain. To find the value of one yard of cloth; fay, As £100 A's gain: 30 his stock:: 128 B's gain: £388s. then, inversely, As 10 months: 13885.:: 8 months: 648 the value of the whole cloth. As 80 yds.: £48 :: 1 yd.: 12s. answer. Now, to find the value of a dollar; As ₤ 100 A's gain : 30 his stock:: ₤87 10s. C's gain: £26 5s. then, inversely, As 10 months: ₤2655.:: 7 months: £37 105. =120 dollars. Lastly, As 120 dollars: £37 Ios.:: dollar: 6/3 anfwer. FELLOWSHIP BY DECIMALS. RULE. Divide the whole gain, or lofs, by the whole stock; and the quotient multiplied severally by each man's stock, will give the gain, or lofs, of each. EXAMPLES. 1. A, B and C companied; A put in 1200, B, 150, and C, 50, with which they gained 8co; what is the share of each? Ans. 800-400=2; then 200×2=£400=A's gain, 150×2=300=B's gain, and 50×2=100=C's gain. 2. A, B, C and D trade, and gain £200, which is to be divided in the following manner, viz. So often as A has £6, B must have 10, C, 14, and D, 20; what is the fhare of each ? 200 6+10+14+20=50, and 4, quotient; then 6x4=€24 A's gain; 10×4=£40 B's gain; 14×4 =56 C's; and 20 × 4 = 180 D's gain. 3. A, 3. A, B and C companied; A put in £40 55. B, £80 10s. and C, £161, with which they gained 120; what is each man's share of the gain ? Sum total = 281,75) 120,000000(,4259+ Proof. A's gain £17 25. 10d. + B's gain £3455. 3d. +C's gain £68 11s. 44d. = £119 195. 11d. PRACTICE Is a contraction of the Rule of Three direct, when the first term happens to be an unit, or one; and has its name from its daily use among Merchants and Tradesmen, be |
