5. To take 4 per cent. of a number, is to take how many hundredths of the number? 6. What part of a number is 2 per cent. of a number? SOLUTION.-2 per cent. is ro, or; hence, 2 per cent. of a number is of the number. 7. What part of a number is 4 per cent. of it? 5 per cent. of it? 10 per cent. of it? 8. What part of a number is 20 per cent. of it? 40 per cent. of it? 50 per cent. of it? 9. What per cent. of a number is expressed by 10%? By ? By 188? 75 10. What per cent. of a number is .06 of it? Is .30 of it? Is .75 of it? Is 1.25 of it? DEFINITIONS. 409. Any Per Cent. of a number is so many hundredths of the number. The term per cent. is a contraction of per centum, which means by the hundred. 410. The Rate per cent. is the number denoting the number of hundredths. 411. The Sign of per cent. is %, and is read per cent. Thus, 1 100 6 ;, or .01, may be written 1%, and read one per cent. 100' 42 100 115 100' , or .06, , or 1.15, 412. The Base is the number or quantity of which the per cent. is computed. 413. Percentage is the process of computing by hundredths. The term Percentage is applied, also, to that part of the base which corresponds to the rate per cent. Base and Rate Per Cent. given, to find the Percentage. 415.-1. What part of a number is 4% of it? SOLUTION.-4% is 1, or ; hence, 4% of a number is of the number. 2. What part of a number is 15% of it? 30% of it? 3. What part of a number is 20% of it? 12% of it? 50% of it? 4. What is the simplest form of 20%? SOLUTION.-20% is %, which in its simplest form is . 5. What is the simplest form of 50%? Of 60% ? Of 80%? 6. What is the simplest form of 121%? Of 16% ? Of 331% ? 7. A farmer had 20 cows, and sold 10% of them. How many did he sell? 8. If from a flock of sheep 5% of them should be taken, what per cent. would remain? 9. A man bought a horse for $100, and sold him at a profit of 25%. For what sum did he sell him? 10. If you buy a horse for $100, and sell him at a loss of 20%, how much do you get for him? WRITTEN EXERCISES. 416.-1. What is 7% of 9546 yards? 9546 yds. .07 668.22 yds. SOLUTION. Since 7% is .07, 7% of 9546 yards is .07 of 9546 yards, which is 668.22 yards, the percentage required. 2. What is 5% of 860 pounds? 3. What is 12% of 750 men? 417. Rule for Finding any Per Cent. of a Number.—Multiply the given number by the rate per cent. expressed decimally. PROBLEMS. 418. How much is 1. 4% of $61.50? 7. 19% of 562 ? 2. 31% of $974? 3. 74% of 160yd.? 4. 25% of 530rd.? 5. 1% of 9160? 6. 31% of 850? 8. 12% of 880? 9. 10% of $750? 10. 8% of 450 men? 11. 15% of 560cwt.? 12. 60% of 725lb.? 13. If you earn in a year $300, and spend 45% of that sum, how much do you spend? 14. What is a merchant's commission for selling goods to the amount of $7500, at 21% ? 15. Of a cargo of corn, consisting of 2560 bushels, 15% was damaged. How much was not damaged? 16. If a town having 9540 inhabitants should increase in population 20%, what would be the number of its inhabitants? CASE II. Base and Percentage given, to find the Rate Per Cent. 419.-1. What per cent. of a number is of it? What per cent. of 1 is ? I spend ? What per cent. of it did 4. I had $20, and spent $5. What per cent. of my money did I spend? SOLUTION. I had $20, and spent $5; hence, I must have spent ʊ, or of my money; and equals, or 25%. 5. What per cent. of $10 is $2? Of $45 is 30? 6. 8 days are what per cent. of 20 days? Of 48 days? 7. I received $3 for collecting $60. What per cent. did I receive? 8. A farmer bought a cart for $50, and sold it for $60. What per cent. did he gain? 9. James bought a knife for $.60, and sold it for $.48. What per cent. was the loss? 10. What per cent. does a merchant gain who buys flour at $8 per barrel, and sells it at the rate of 3 barrels for $30? WRITTEN EXERCISES. 420.-1. What per cent. of 400 is 24? 400)24.00(.06=6% 24.00 SOLUTION.-Since 24 is of 400, it is .06, or 6%, of 400, which is the rate per cent. required. 2. What per cent. of 520 is 26 ? 3. What per cent. of 95 bushels are 3.6 bushels? 421. Rule for finding the Rate Per Cent. that a given Percentage is of the Base.-Divide the percentage by the base, extending the quotient to hundredths. PROBLEMS. 422. What per cent. of― 1. 54 yards are 9 yards? 7. 560 is 106.4? 8. 725 is 435? 9. $756 are $75? 10. 450 men are 36 men 11. 560cwt. are 84cwt.? 12. 725lb. are 435lb.? ? 13. If you earn $300, and spend $135 of it, what rate per cent. of the sum earned is the sum spent? 14. A house, which cost $5670, was sold for $283.50 above the cost. What was the rate per cent. of gain? 15. Of an army of 45450 men, 12626 men were lost in battle. What was the rate per cent. of loss? 16. If a horse, which cost $250, was sold for $100 above cost, what was the rate per cent. gained? 17. A certain town, which had 9540 inhabitants, has increased by 1908 persons. What is the rate per cent. of increase? |