4. How many dollars in 240 guineas? Ans. $1226.358. Ans. 1059.03 fr, Ans. £34 14.03+s. Ans. 6937.568 marks. 8. How many pounds in 4375 marks? Ans. £214 8 s. 3 d.—. 9. How many pounds Avoirdupois in 1000 sovereigns? Ans. 17.6104. 10. An ingot of pure gold was brought from California to be coined at the Philadelphia mint; if it weighed 15 lb. 8 oz. Troy, how many gold dollars will it make, of the coin being alloy? Ans $3886; 7.08 gr., rem. MISCELLANEOUS PROBLEMS. 1. How many planks laid crosswise, 1 ft. wide, will it take for a board walk 1 mi. 16 rd. long, and 4 ft. wide? Ans. 5544. 2. How many bushels of grain can a farmer store in a hogshead containing 122 gallons? Ans. 13.1+bu. 3. How much stair carpet will be required for a flight of 18 steps, each 10 in. wide and 7 in. high? Ans. 8 yd. 4. The cost of digging a sewer 1 miles long, 5 feet wide, and 8 ft. deep, was $3716; what was the yard? 5. A farmer has a mow 20 ft. long, 12 ft. deep; how many tons of hay does it hold? price per cubic Ans. $.31. wide, and 10 ft. Ans. 6 tons. 6. From a quartz rock yielding silver at the rate of $123.75 per ton, a miner obtained $75.64 worth; what was the weight of the rock? Ans. 12 cwt. 224 lb. 7. If 4 persons can stand on one square yard of ground, how many people can be contained, in a public square 32 rods on each side? Ans 123904. 8. How many bunches of lath will be required for the walls and ceiling of a room 18 ft. long, 14 ft. wide, 10 ft. high, each bunch being estimated to cover 5 sq. yd.? Ans. 1937. 9. I wish to carpet my parlor 25 ft.X17 ft. with Brussels carpet 26 in. wide; what will it cost me at $1.87 per yard, the strips running lengthwise and the pattern requiring an allowance of 31 yd. for matching? Ans. $131.25. 10. A street 36 ft. wide, was pavel with Nicholson pavement at $3.25 per square yard; what did it cost to pave a square 32 rods long? Ans. $6864. 11. A railroad tunnel is one-eighth of a mile long, averaging 24 ft. wide and 20 ft. high; what did the excavation cost, at $1.50 a cubic yard? Ans. $17600. 12. How many freight cars will be required to transport 2000 bu. wheat, 24000 lb. being the weight allowed for a single car? Ans. 30 cars. 13. A coal-dealer has a wagon which holds exactly one ton of Schuylkill red ash coal (36 cu. ft.); if the wagon-bed is 7 ft. long and 41 ft. wide, what is its depth? Ans. 12 in. 14. I used the earth taken from 4 cellars in grading a lot of ground; if the cellars were 30×21 ft., 28×18 ft., 24×16 ft., and 32×24 ft., respectively, and 5 ft. deep, how much earth did I use? Ans. 423 loads. SUPPLEMENTARY EXAMPLES. To be omitted unless otherwise directed. 15. What costs the excavation for a cellar 51⁄2 feet deep under the main building of a dwelling-house 30×25 ft. and an excavation for the walls of an L 16 ft. square, 11⁄2 ft. wide, and 2 ft. deep, at 50 per cubic yard? Ans. $78.88. 16. What costs the plastering of a house of 12 rooms, there being on each story 4 rooms 14 X 15 ft. and a hall 30×8 ft.; the first story being 10 ft. high, the second 9 ft., and the third 8 ft., allowance being also made for 24 doors 7 × 31⁄2 ft., and 30 windows 6×3 ft., at 30% per sq. yd.? Ans. $357.863. 17. Required the cost of a cellar of a house 40 X 30 ft., the different items being as follows: excavating cellar, 4 ft. deep at 50% per cu. yd.; cellar wall, 7 ft. high and 18 in. thick, the lower 4 ft. common masonry, @$3.15 a perch, and the upper 3 ft. cut stone at 169 per sq. ft. 18. Required the cost of the brick-work of the same house, the walls being 35 ft. high and 13 in. thick, and gable 10 ft. high, using common bricks at $10 per M., bricklaying costing $3 per M., allowing for 3 doors, each 7 ft. by 3 ft., and 30 windows each 6 ft. by 3 ft. Ans $1258.915 INTRODUCTION TO PERCENTAGE. MENTAL EXERCISES. 1. A gain of $2 on $5 is a gain of how many dollars on the hun dred? SOLUTION.-If the gain on $5 is $2, on $100, which is 20 times $5, the gain is 20 times $2, or $40. 2. A gain of $3 on $5 is a gain of how many dollars on the hundred? 3. What is the gain on a hundred when the gain is 4 on 20? 20? 4 on 25? 5 on 4. If the gain on $100 is $25, what is the gain on $4? on $12? on $20? 5. If the gair on $100 is $20, what is the gain on $5? on $15? on $25? 6. If the gain on $100 is $40, what is the gain on $1? on $12? on $36? 7. If the gain on $100 is $25, what part of the $100 equals the gain? 8. If the gain on $100 is $40, what part of the $100 equals the gain! 9. If the gain on $24 is at the rate of 25 on the 100, what is the gain? 10. If the gain on $25 is at the rate of 20 on the 100, what is the gain? 11. What is the gain on $50 at the rate of 10 on the hundred? 16. Per cent. means the same as per hundred; what then can we call the rate per hundred? Ans. Rate per cent. 17. A gain of $20 on $80 is a gain of what per cent.? 18. A loss of $15 on $75 is a loss of what per cent.? 19. What per cent. is a gain of 20 on 40? 5 on 25? 4 on 80? 3 on 60? 8 on 200? 20. What is 5 per cent. of 80? 4 per cent. of 24? 20 per cent of 40? 25 per cent. of 48? SOLUTION.-5 per cent. is at the rate of 5 on the 100, and since 5 is of 100, 5 per cent. of 80 is of 80, which is 4. 21. What is 50 per cent. of 24? 30 per cent. of 60? 40 per cent of 35? 60 per cent, of 45? 22. What per cent. is a gain of 15 on 60? 18 on 72? 12 on 48? 16 ov 80? 20 on 60? 15 on 90? SECTION VIIL PERCENTAGE. 376. Percentage is the process of computation in which the basis of comparison is a hundred. 377. The Term per cent.-from per, by, and centum, a hundred-meaus by or on the hundred; thus, 6 per cent. of any quantity means 6 of every hundred of the quantity. 378. The Symbol of Percentage is %. The per cent. may also be indicated by a common fraction or a decimal; thus 6%==.06. 379. The Quantities considered in percentage are the Base, the Rate, the Percentage, and the Amount or Differ ence. 380. The Base is the number on which the percentage is computed 381. The Rate is the number of hundredths of the base which are taken. 382. The Percentage is the result obtained by taking a certain per cent. of the base. 383. The Amount or Difference is the sum or difference of the base and percentage. They may both be em braced under the general term Proceeds. NOTE. In computation the rate is usually expressed as a decimal. For the difference between Rate and rate per cent., see Brooks's Philosophy of Arithmetic. EXPRESSION OF THE RATE. 1. Express 4% as a decimal and common fraction. SOLUTION. Since per cent. is so many on a hundred, 4% of a quantity is .04 of it; or, as a common fraction, or of it. OPERATION. 4%.0418025. 384. Cases. The subject of percentage is conveniently treated under three distinct cases: 1. Given the rate and base, to find the percentage or proceeds. 2. Given the rate and percentage or proceeds, to find the base, 3. Given the base and percentage or proceeds, to find the rate. NOTE.-Authors usually present the subject in five or six cases, but it is thought that the method here adopted is to be preferred, on account of its logical accuracy and practical convenience. CASE I. 385. Given, the base and the rate, to find the percentage or the proceeds. 1. What is 6% of $275? What is the amount of $275, increased by 6% of itself? SOLUTION.-6% of $275 equals .06 times $275, which, by multiplying, we find to be $16.50. SOLUTION.--A number increased by 6%, or .06 times itself, equals 1.06 times itself; 1.06 times $275 equals $291.50. OPERATION. $275 .06 $16.50 OPERATION. $275 1.06 $291.50 Rule I.-Multiply the base by the rate, to find the percentage. Rule II.—Multiply the base by 1 plus the rate, to find the amount; or by 1 minus the rate, to find the difference. NOTES.-1. When the rate gives a small common fraction, take such a part of the base as is indicated by this fraction. 2. The amount equals the base plus the percentage; the difference equals the base minus the percentage. EXAMPLES FOR PRACTICE What is 2. 12% of 475? Ans. 57. |