23. What per cent of the 800 paper mills of this country does New York State contain, if it contains 180 paper mills? 24. In a certain school there are 752 pupils, of whom 282 are in the high school department. What per cent of the pupils are in the high school? 25. In crossing the Atlantic a vessel used 3570 of the 4760 tons of coal on board. What per cent of the supply was used? 26. A man who owed $20,000 could pay only $4900. What per cent of his debts could he pay? 27. Of 6225 baskets of fruit shipped from Delaware to New York, 2739 were spoiled by a delay. What per cent of the fruit was spoiled? 28. A certain mining town contains 4160 inhabitants, of whom 3640 are miners. What per cent of the population are miners? 29. In a recent year there were 210,000 miles of ocean cable in the world, of which 40,600 were in the Atlantic Ocean. What per cent of the cable was in the Atlantic? 30. A 20-dollar gold coin was so badly worn that it had lost 10 cents in value. What per cent of its weight had been worn away? 31. In a year when there were 270,000 Indians in the United States, 60,000 of them could speak English. What per cent of the Indian population could speak English? 32. The United States one year produced 20,600,000 barrels of salt, of which Michigan furnished 7,725,000 barrels. What per cent of the whole did Michigan produce? 33. A manufacturing business valued at $225,000 is owned. by three partners: Hale, Chesley, & Hoit. If Mr. Hale's share is $140,625, Mr. Chesley's $56,250, and Mr. Hoit's $28,125, what per cent of the business does each man own? 304. Finding a number when a per cent of it is given. What is the number? 1. If of a number is 9, what is of it? 2. If of a number is 21, what is If 7% of a number is 21, what is 1% of it? 3. If 15% of a number is 30, what is 1% of it? What is the number? How does this result compare with 30÷.15? In what two ways, then, may we find a number, if 15% of it is given? 4. 6% of a number is 24. Find the number in two ways. 5. If 331%, or 3, of a number is 4, what is the number? 75%, or, of a number is 15, what is the number? If 16. If 50% of a man's working day is 42 hours, how many hours per day does he work? 17. A baseball team lost 8 games, or 25% of the total number of games played. How many games were played? 18. When a ring is 16 carats fine, it is 663 % pure gold. If the ring were pure gold, how many carats fine would it be? 19. How many sweet potato plants does it take to yield a barrel of sweet potatoes, if 25 plants yield 20% of a barrel? 20. How much mail and express matter passes through the Grand Central Station, New York, each day, if 331 % of it, or 300 tons, is mail matter alone? 21. If a fast freight goes 20% of its journey from New Orleans to Louisville in 10 hours, how long does the trip take? 22. If it takes 25% of a man's salary to pay his rent, which is $15 a month, what is his monthly salary? 23. When a grocer had sold 40% of a case of eggs, 12 dozen had been sold. How many dozen eggs did the case hold? 24. A fruit dealer sold 37% of a box of grapefruit. How many did the box contain at first, if he sold 24? 25. Find the total weight of a bale of sponges from Florida, if the covering weighs 2 pounds, or 4% of the total weight. 26. It requires 120 tons of wood pulp to make the paper necessary to supply a certain newspaper for one day. If this is 80% of the weight of the paper, how many tons of paper are used per day? WRITTEN EXERCISES 306. 1. Find the number of which 84 is 24 %. SOLUTION. that is, Hence the number 2. Find the number of which 273 is 871 %. SOLUTION. Hence, Or, to shorten the work, 3. 225 is 15 % = 8 times 39, or 312. 39 8 = of 273 = 312. 7 6% 8. $24.84 is 5. 384 is 25% 10. $43.47 is 42 % 11. $93.60 is 64% 6. 504 is 28 % 18. 13. $ 1.14 is % 15. $79.62 is 371 % 17. $90.97 is 1831 % A manufacturer received 500 pounds of yarn, which was 8% of his order. How much yarn had he ordered? 19. How much steel was used in constructing the Chicago government building, if 12% of it, or 1200 tons, was used in the dome? 20. In six hours 6000 tons of coal were loaded on a vessel. If this was 80% of her load, how many tons did she carry ? 21. A quantity of rice lost 20% of its weight in being hulled at the mill. If the hulls weighed 4752 pounds, what was the weight of the rough rice? 22. When 6875 tons of ice had been put into an ice house on Lake Erie, 62% of its capacity was occupied. Find the capacity of the ice house in tons. 23. If the shrinkage of a quantity of wheat in drying was 2% and amounted to 775 pounds, how much did the wheat weigh before drying? 24. If 32% of the people in a certain city are voters, and there are 40,176 voters, find the population of the city. 25. It is estimated that by skimming cream from milk only 80% of the butter is obtained. If the modern method of separating extracts all of the butter, what should be the yield of a cow that by the old method produced 180 pounds of butter per year? 26. A grocer bought 65 dozen ears of green corn at 12¢ per dozen. If this was 75% of the sum for which he sold the corn, how much did he receive for it? 27. A barrel of flour weighing 196 pounds sold at the grocery for 3 per pound, which was 140 % of the cost. Find the cost. 28. How many feet of barbed wire are there on a spool, if 12 feet is % of it? 29. If the productive area of coal in the United States is 154,220 square miles, or 55% of the entire coal area, what is the extent of the coal fields in this country in square miles? 307. Summary. You have learned how to find: a per cent of a number; what per cent one number is of another; and a number when a per cent of it is given. 308. The number of which a per cent is found is called the base. 309. The number of hundredths found is called the rate, or rate per cent. 310. The result obtained by finding a per cent of the base is called the percentage. Thus, in 5% of $120 = $6, $120 is the base, 5% is the rate, and $6 is the percentage. $120 $6, or $126, is the amount; $120-$6, or $114, is the difference. 311. We may now express in brief form the principles learned in the preceding pages: The percentage equals the base multiplied by the rate. WRITTEN EXERCISES 312. 1. Given the base 245, and the rate 8%; find the percentage. 2. If the percentage is $5.50 and the base $22, find the rate. 3. Find the base, if the percentage is $75 and the rate 4%. |