1. If 4 men earn $24 in 7 days, how much can 14 men earn in 12 days? OPERATION. 12 14 X$24=144 ANALYSIS.-If 4 men earn $24 in 7da., 1 man will earn of $24, and 14 men will earn of $24. If 14 men earn of $24 in 7da., in 1 day they will earn 4 of 14 of $24, and in 12da. they will earn of of $24, which, by cancelling and multiplying, equals $144. SOLUTION.-Here the sum they can earn is in proportion to the number of men and the time they labor, hence the sum is to $24 as 14 men to 4 men, and 12 days to 7 days; hence we have the compound proportion as stated in the margin, from which we find the unknown term by the principles of compound proportion. NOTE. The comparison may be abbreviated thus: If 4 men earn $24, 14 men will earn of $24. If they earn it in 7da., in 12da. they $144. will earn of of $24 2. If 36 men earn $324 in 18 days, how much will 42 men earn in 27 days? Ans. $567. 3. If a company of 96 men eat 7281b. of meat in 21 days, how much will a regiment of 1050 men eat in 36 days? Ans. 13650lb. 4. If 58 cows eat 29 bundles of hay in 25 days, how many cows will eat 35 bundles in 14 days? Ans. 125 cows. 5. If 12 men in 35 days build a wall 140rds. long, 6ft. high, how many men can in 40 days build a wall of the same thickness 144 rods long, 5ft. high? Ans. 9 men. 6. If 18 carpenters build a house in 45 days, working 12h. a day, in how many days would 36 carpenters have built it, working 10h. a day? Ans. 27 days. 7. If 28 men dig a trench 120 rods long, 15 feet wide, and 12 feet deep, how many men will dig a trench 360 rods long, 9 feet wide, and 10 feet deep? Ans. 42 men. 8. If 8 yards of muslin, 14yd. wide, cost $1.25, what should be paid for 10 yards of the same quality, lyd. wide? Ans. $1.40g. 9. If 35 horses can eat a lot of grain in 36 days, in what time will 3 times as much grain be consumed, if 5 horses are added when the grain is eaten? Ans. 104ğda. 10. If 32 men can build 60 rods of wall in 15 days, in what time can they build 75 rods, if 8 men leave when 40 rods have been built? Ans. 21 da. 11. How many cows can you get for 60 horses, if 3 horses are worth 45 sheep, and 4 cows are worth 12 sheep? Ans. 300 cows. 12. How long will it take 4 horses to plough a field, if 8 horses do as much as 12 mules, and 15 mules do as much as 20 oxen, and 12 oxen do it in 20 days? Ans. 30da. 13. If 147 loaves of bread, weighing 6oz. each, cost $8.10 when flour is $7 a barrel, what ought 96 loaves 7oz. each, when flour is worth $9 a barrel? to cost, weighing Ans. $7.93+. 14. If 17 plank, 35ft. long, 28in. wide, and 6in. thick, cost $68, what will 40 plank, 32ft. long, 25in. wide, and 7in. thick, cost, when lumber is worth more per foot? Ans. $182.85%. 15. If $600 in 4yr. 6mo. at 6 per cent. gain $162 interest, how much interest will $800 gain in 6yr. 4mo. at 8 per cent.? Ans. $105. 16. If from a dairy of 24 cows, each giving 18qt. of milk daily, 10 cheeses of 60lb. each are made in 12 weeks, how many cows will produce 40 cheeses of 75lb. in 9 weeks, if they give 12qt. each? Ans. 240 cows. 17. If 24 men, in 15da. of 12h. each, dig a trench 300rd. long, 5yd. wide, 6ft. deep, in what time can 45 men, working 10h. a day, dig a trench 125rd. long, 15ft. wide, 8ft. deep? 18. If 50 men can build 50 rods of wall in 75 men will be required to build 80 rods of wall as high in 40 days? Ans. 51da. days, how many as thick and Ans. 180 men. SECTION IX. PERCENTAGE. 255. Percentage is the process of computation in which the basis of comparison is a hundred. 256. The term per cent. means by or on a hundred; thus, 5 per cent. of anything means 5 of a hundred, whatever be the denomination. 257. Since per cent. is so many of a hundred, 1 per cent. of a number is 10 of it, 2 per cent. is 7% of it, 5 per cent. is Too of it, etc. It is also evident that 100 per cent. of a number is the whole number. 258. The character % is used to represent the words per rent. The per cent. may also be indicated by a common fraction or a decimal; thus, 5 per cent. or 5% 150.05. 259. In percentage there are four quantities considered: 1. The Basis, or number on which percentage is estimated. 2. The Rate, or number denoting how many of a hundred. 3. The Percentage, denoting how many of the basis. 4. The Amount or Difference of the basis and percentage. CASE I. 260. Given the basis and rate, to find the percentage. 1. What is 6 per cent. of $320? SOLUTION.-100 per cent. of $320 is $320, hence 1 per cent. of $320 is to of $320, and 6 per cent. is 6 times Too of $320, or ro of 6 times $320, which we find is $19.20. σ OPERATION. $320 .06 $19.20, Ans. SOL. 2D.-6 per cent. of $320 is † of $320, which equals д of 6 times $320, which, by multiplying by 6 and dividing by 100, we find is $19.20. RULE.-Multiply the basis by the rate and divide the product by 100. NOTE.-It is often simpler to take such a fractional part of the basis as is indicated by the rate. Thus, 25% of 40 equals or of 40, which is 10. See Normal Mental Arithmetic. 17. How much is 421 per cent. of 61b. 8oz. 12pwt.? 18. A man bought a horse for $180, and sold it at a gain of 12 per cent.; what did he gain? Ans. $21.60. how many barrels remained? 19. A bought 6000bar. of flour, and sold 163 per cent. of it; Ans. 5000bar. 20. B bought 1016 acres. of land, and sold 12 per cent. to C, and 37 per cent. of the remainder to D; how much remained? Ans. 555 acres. 21. Mr. Hamlin had 360 acres of land, and sold of 331 per cent. of it; how much remained? Ans. 288 acres. 22. 16 per cent. of $5000 is of what A gave for a farm, and the farm cost 3 times as much as his house; required the cost of the house. Ans. $624. ៖ 23. What is the sum of 20 per cent. of 183 per cent. of 780 dollars, and 20 per cent. of 25 per cent. of 488 dollars? Ans. $53.65. 24. A having of 900 acres of land, sold 15 per cent. of it to B, and 163 per cent. of the remainder to C; how much did he retain ? Ans. 510 acres. 25. A's salary is $2000 a year; he spends 10 per cent. of it the 4 first quarter, 15 per cent. the second, 6 per cent. the third, and per cent. the fourth; how much did he save? Ans. $1300. 26. A and B bought together 1521 acres of land, of which A bought as many as B; A sold B 331 per cent. of his land, and then bought 333 per cent. of B's; how many acres had each then? Ans. A, 767; B, 751. CASE II. 261. Given the percentage and rate, to find the basis. 1. 60 is 5 per cent. of what number? SOLUTION. If 60 is 5 per cent. of some number, 1 per cent. of that number is of 60, which is 12, and 100 per cent. of the number equals 100 times 12, which is 1200. SOLUTION 2D.-If 60 is 5 per cent. of some number, then 13 or of that number equals 60, and 8 of the number equals 20 times 60, which is 120. OPERATION. 5%=60 1%=12 100% 1200, Ans. OPERATION. = 60 8=1200, Ans. RULE.-Multiply the percentage by 100 and divide by the rate. NOTE. The second method of solution is preferable when the rate will give a fraction with small terms. Ans. 225. Ans. 1740. Ans. 300. Ans. 280. Ans. 1520 2. 45 is 20 per cent. of what number? 3. 87 is 5 per cent. of what number? 4. 75 is 25 per cent. of what number? 5. 112lb. is 40 per cent. of what weight? 6. 456 acres is 30 per cent. of how many? 7. $645 is 621 per cent. of what sum? 8. $450 is 124 per cent. of what sum? 9. 5is 33 per cent. of what fraction? 10. 73 is 75 per cent. of what number? 11. 42A. 2R. 32P. is 163 per cent. of how much land? 12. The percentage is 85, the ratio 20; what is the basis? Ans. $1032. Ans. §. Ans. 425. 13. A spends $600 per year, which is 24 per cent. of his salary; required his salary. Ans. $2500. 14. A man bought some flour and sold 25 per cent. of it to A, and 33 per cent. of the remainder to C; how much did he buy if he sold C 640 barrels ? Ans. 2560bar. |