3. If 6 men consume 1 barrel of flour in 30 days, how much would 48 men consume? It is evident that of a barrel would be the amount consumed by 1 man; hence, 48. times is the amount consumed by 48 men. OPERATION. X48 8. Ans. 8. 4. If of a barrel of flour cost of a dollar, what will cost? Ans. $1. 5. if I walk 84 miles in 3 days, how far should I walk at the same rate in 9? Ans. 252. 6. f 8lb. of sugar cost $1,28, how much will 13. cost? What is 16 x 13? Ans. $2,08. 7. If of a piece of cloth cost $8,25, what will cost? Ans. $24,75. 9. If 300 barrels of flour cost $570, what will 200 cost? What is 570 ? Ans. $380. 10. If of a barrel of cider cost of a dollar, what will cost? What is 2×? Ans. $18. OF QUESTIONS REQUIRING. TWO STATEMENTS. 440. 145. The answer to each of the above questions has been found by a single statement. Questions, however, frequently occur in which two or more statements are necessary. In most Arithmetics, such questions are arranged under a rule called Compound Proportion, or the Double Rule of Three. They can, however, be answered by the rules already given. EXAMPLES. 1. If a family of 6 persons expend $300 in 8 months, how much will serve a family of 15 persons for 20 months? First question. If OPERATION. $300 will support a persons. persons. family of 6 persons for 8 months, how many dollars will support 15 persons for for the same time? 6: 15 :: 300 : Ans. 15 6(4500 Ans. $750 2. If 16 men build 18 feet of wall in 12 days, how many men must be employed to build 72 feet in 8 days, working at the same rate? The first question is, how long would it take the 16 men to build the 72 feet of wall. It is evident that 18 feet of wall, is to 72 feet, as 12 days, the time necessary to build 18 feet, is to 48 days, the time necessary to build 72 feet. The second question is, if 16 men can build 72 feet of wall in 48 days, how many men are necessary to build it in 8 days? Make 16 men the third term. Then as the same work is to be done in less time, more men will be necessary; therefore, the fourth term will be greater than the third, and hence 8 days are placed in the first term (see § 142). 3. If a man travel 217 miles in 7 days, travelling 6 hours a day, how far would he travel in 9 days, if he travelled 11 hours a day. OPERATION. 1st. days. days. 7 : 9 OPERATION. miles. miles. hours. hours. miles. miles. :: 217 : 279 6: 11 :: 279 : 511 4. If a pasture of 16 acres will feed 6 horses for 4 months, how many acres will feed 12 horses for 9 months? Ans. 72. 5. If the wages of 6 men for 14 days be $84, what will be the wages of 9 men for 11 days? Ans. $99. 6. If 154 bushels of oats serve 14 horses for 44 days, how long would 406 bushels last 7 horses? Ans. 232 days. 7. If 25 men can earn $6250 in 2 years, how long will it take 5 men to earn $11250? Ans. 18 years. 8. If a barrel of beer last 7 persons 12 days, how much will be drank by 42 persons in a year? Ans. 182bar. 18gal. 9. If 9 men can cut 36 acres of grass in 4 days, how many acres will 19 men cut in 11 days? Ans. 209 acres. 10. If 25 persons consume 300 bushels of corn in 1 year, how much will 139. persons consume in 7 years at the same rate? Ans. 11676bu. 11. If 32 men build a wall 36 feet long, 8 feet high, and 4 feet wide in 4 days; in what time will 48 men build a wall 864 feet long, 6 feet high, and 3 feet wide? Ans. 36 days. REDUCTION OF CURRENCIES. § 146. Previous to the act of Congress which established a uniform currency throughout the United Sates, in dollars, dimes, cents, and mills, each State had its own particular currency. This circumstance has caused the dollar to be divided differently in the different States, though the real value of it is the same in all. Q. How was the currency of the United States established? What are its denominations? Is the value of a dollar the same in all the states? How many shillings make a dollar in English Currency? In Canada Currency? In New York Currency? In New England Currency? In Pennsylvania Currency? In Georgia Currency? CASE I. 147. To reduce a sum in either currency to Federal Money. The reduction of these currencies to Federal Money consists in this having given any sum expressed in pounds shillings and pence, to find its value in dollars cents and mills. Take, for example the English Currency. £1 20s 240d. $1 4s 6d=54d. Hence, £1 $1 :: 240: 54, and consequently, £1-$1 x 240-$1x40; 54 that is, £1 is equal to 40 of a dollar, which being reduced to dollars and the decimal of a dollar gives £1 $4,444+. If we now multiply each side of the equality 9 £2=$1x40x2, £4=$1×40×4, £3=$1×40×3 £5 $1×18×5, and generally, any number of pounds will be brought into dollars by multiplying by 40. As similar reasoning may be employed for all the currencies, we have the following RULE. -I. Reduce the given sum to the decimal of a pound as in $135. II. Find the value of £1 in the fraction of a dollar. III. Multiply the given sum by this fraction and the product will be the value in dollars. EXAMPLES. 1. Change £27 3s 9d to Federal Money. Having reduced reduced the pounds, shillings, and pence to the decimal of a pound, we bring the whole to dollars by multiplying OPERATION. 3s 9d £0,1875. £27 3s 9d £27,1875. 27,1875x40=120,83 3+. Ans. $120,83 3+: by 40 and dividing the product by 9. 2. Change £140 18s 9d to Federal Money. Ans. $626,38 8+. By an act of Congress passed in 1832, the value at which the English pound is to be received and estimated at the custom-house, was fixed at $4,80. If we assume this as the value of the English pound, we have £1 : $1 :: 480: 100; hence, £1 $1x480-$1x2 = therefore, pounds will be brought to dollars by multiplying by 24 and dividing by 5. 1. Reckoning the pound at $4,80, how many dollars in £49 8s 6d? OPERATION. £49 8s 6d £49,425. 49,425 × 24237,24. Ans. $237, 24. We first bring the sum to pounds and decimals of a pound. We next multiply by the multiplier 24 we then reduce the product to pounds, shillings, and pence. |