EXAMPLE. From a lot of boiler tubes 76% were used in the construction of a boiler. If there were 72 tubes unused, how many tubes were in the lot? SOLUTION.-Here 72 is the difference and 76% is the rate. Applying rule, 72 ÷ (1 − .76) = 300 tubes. Ans. EXAMPLE. The theoretical number of foot-pounds of work per minute required to operate a boiler feed-pump is 127,344. If 30% of the total number actually required be allowed for friction, leakage, etc., how many foot-pounds are actually required to work the pump? SOLUTION. Here the number actually required is the base; hence, 127,344 is the difference, and 30% is the rate. Applying the rule, 127,344 ÷ (1 — .30) = 181,920 foot-pounds. Ans. 192. EXAMPLE.-A certain chimney gave a draft of 2.76 inches of water. By increasing the height 20 feet the draft was increased to 3 inches of water. What was the gain per cent.? SOLUTION.-Here it is evident that 3 inches is the amount and that 2.76 inches is the base. Consequently, 32.76.24 inch is the percentage, and it is required to find the rate. Hence, applying rule 23, gain per cent. = .24 ÷ 2.76.0878.7%. Ans. 193. EXAMPLE.-A certain chimney gave a draft of 3 inches of After an economizer had been put in the draft was reduced to 1.2 inches of water. What was the loss per cent.? water. SOLUTION.-Here it is evident 1.2 inches is the difference (since it equals 3 inches diminished by a certain per cent. loss of itself) and 3 inches is the base. Consequently, 3 1.2 1.8 inches is the percentage. Hence, applying rule 23, = loss per cent. = 1.8 3.60 60%. Ans. 194. To find the gain or loss per cent.: Rule 28. Find the difference between the initial and final values; divide this difference by the initial value. EXAMPLE. If a man buys a steam engine for $1,860 and some time afterwards purchases a condenser for 25% of the cost of the engine, does he gain or lose, and how much per cent., if he sells both engine and condenser for $2,100 ? SOLUTION.-The cost of the condenser was $1,860 x .25 sequently, the total initial value, or cost, was $1,860 + $465 Since he sold them for $2,100, he lost $2,325 $2,100 $225. applying rule, $465; con$2,325. Hence, 1. A steam plant consumed an average of 3,640 pounds of coal per day. The engineer made certain alterations which resulted in a saving of 250 pounds per day. What was the per cent. of coal saved? Ans. 7%, nearly. 2. If the speed of an engine running at 126 revolutions per minute should be increased 6%, how many revolutions per minute would it then make? Ans. 134.19 revolutions. 3. The list price of an engine was $1,400; of a boiler, $1,150, and of the necessary fittings for the two, $340. If 25% discount was allowed on the engine, 22% on the boiler, and 12% on the fittings, what was the actual cost of the plant? Ans. $2,244.50. 4. If I lend a man $1,100, and this is 18% of the amount that I have on interest, how much money have I on interest? Ans. $5,945.95. 5. A test showed that an engine developed 190.4 horsepower, 15% of which was consumed in friction. How much power was available for use? Ans. 161.84 H. P. 6. By adding a condenser to a steam engine, the power was increased 14%, and the consumption of coal per horsepower per hour was decreased 20%. If the engine could originally develop 50 horsepower and required 34 pounds of coal per horsepower per hour, what would be the total weight of coal used in an hour, with the condenser, assuming the engine to run full power? Ans. 159.6 pounds. DENOMINATE NUMBERS. 196. A denominate number is a concrete number, and may be either simple or compound, as 8 quarts, 5 feet, ten inches, etc. 197. A simple denominate number consists of units of but one denomination, as 16 cents, 10 hours, 5 dollars, etc. 198. A compound denominate number consists of units of two or more denominations of a similar kind, as 3 yards, 2 feet, 1 inch; 3 pounds, 5 ounces. 199. In whole numbers and in decimals, the law of increase and decrease is on the scale of 10, but in compound or denominate numbers the scale varies. MEASURES. 200. A measure is a standard unit established by law or custom, by which quantity of any kind is measured. The standard unit of dry measure is the Winchester bushel; of weight, the pound; of liquid measure, the gallon, etc. MEASURES OF EXTENSION. 202. Measures of extension are used in measuring lengths, distances, surfaces, and solids. 1 A. . sq. rd. TABLE 5. 1 square foot = = sq. yd. 1 square yard 1 square rod 1 acre 1 square mile sq. ft. sq. ft. = 640 = 102,400 = 3,097,600 = 27,878,400 = 4,014,489,600 203. The ounce is divided into halves, quarters, etc. Avoirdupois weight is used for weighing coarse and heavy articles. In all the calculations throughout this and the succeeding volumes, 2,000 pounds will be considered one ton, unless the long ton (2,240 pounds) is especially mentioned. 204. Troy weight is used in weighing gold and silver ware, jewels, etc. It is used by jewelers. |