and the marked ones together for a divisor; divide the dividend by the divisor, and the quotient will be the answer in the same denomination the second term was brought into m. ExAMPLEs. 1. If 6 men spend 154 shillings in 7 days, what sum will 8 men spend in 9 days? Stating. Here 154 shillings is of the same kind with the answer, and is therefore made the second term; 6 and 7 are evidently the terms of supposition, and therefore put in the first place; 8 and 9 being terms of demand are put in the third. I then say, If 6 men spend 154 shillings, 8 men will spend more; I therefore mark the less extreme 6 for a divisor: also, If 7 days spend 154 shillings, 9 days will require more; I therefore again mark the less extreme 7. Next I multiply the three unmarked numbers, viz. 154, 8, and 9, together for a dividend, and the product is 11088; and also the two marked numbers 6 and 7 for a divisor, and the product is 42. Dividing the former by the latter, the quotient is 264 shillings, which divided by 20 gives 131.4s. for the answer. 2. If 4 gallons of beer serve 5 persons 6 days, how many days will 7 gallons last 8 persons? Stating. *4 gal. : 6 days : : 7 gal. Earplanation. If 4 gallons serve 6 days, 7 gallons will serve more; I therefore mark the less 4. Again, if 5 persons are supplied 6 days, 8 persons will be supplied (with the same quantity) less than 6 days. I therefore mark the greater extreme 8, and proceed as before. m The truth of this conclusion may be shewn by working the first example according to the rules of simple Proportion, namely, by employing two statings. × 7 same manner every example in the rule may be proved ; and it will furnish a profitable exercise for the industrious student to prove all his operations in this rule by two single rules of three statings. w 137. "Practice is an easy method of solving such rule of three questions as have unity for their first term. The operations consist of Compound Multiplication and Division; and the latter is performed by the given price, &c. taken in aliquot parts of an unit of some superior denomination. 138. One mumber is said to be an aliquot part of another, when the former is contained some number of times exactly in the other; that is, when the former will divide the latter without leaving any remainder. n The rules of Practice are particularly useful to merchants and traders, in computing the value of their commodities. These rules are likewise useful in the Mathematics; and it is on account of their ready and convenient application to the computations, which occur in almost every branch of science, that they are introduced in this place, WOL. I. K 3. If 100l. in 12 months gain 5l. interest, what sum will 80l. gain in 10 months? 5. If a carrier receive 2l. 2s. for the carriage of 3cwt. 150 miles, how much must be paid for the carriage of 7cwt.3gr. 14lb. 100 miles Ans. 3l. 13s.6d. 6. If 10 acres of grass be mowed by 2 men in 7 days, how many acres can be mowed by 24 men in 14 days? Ans. 240 acres. 7. If a man earn 5 shillings a day, what sum will 64 men earn in 124 days Ans, 200l. 8. If 100l. in 12 months gain 31, interest, in what time will 75l. gain ll. 13s. 9d. Ans. 9 months. 9. If 13cvt. be carried 20 miles for 21, 10s, what weight can I have carried 50 miles for 31, 3s. 6d. Ans, 6cwt. 24r. 11b. 162 rem. 10. If 150l. gain 3l. 7s.6d. in 9 months, what sum will gain 3!, in 19 months Ans, 100l. 11. If 3 horses eat 12 bushels of oats in 16 days, how many quarters will 200 horses eat in 24 days? Ans. 150 quarters. 12. If 24 men can build a wall in 36 days, how many men would be required to do 5 times as much work in 3 days? Ans. 1440 men. 137. "Practice is an easy method of solving such rule of three questions as have unity for their first term. The operations consist of Compound Multiplication and Division; and the latter is performed by the given price, &c. taken in aliquot parts of an unit of some superior denomination. 138. One number is said to be an aliquot part of another, when the former is contained some number of times exactly in the other; that is, when the former will divide the latter without leaving any remainder. |