2. A house rents for $630, which is 9% of its value. Find its value. Statement of Relation: 9% of (value of the house) = $630 630 is a product and .09 one of its factors. How may we find the other factor? 3. A merchant gained $19 on an article that cost $95. The gain was what per cent of the cost? 19 is a product and 95 one of its factors. Find the other factor. 258. In finding the rate per cent, or number of hundredths, how many decimal places must there be in the quotient? Then how must the number of decimal places in the dividend compare with the number of decimal places in the divisor? Summary Before dividing, to find the rate per cent, arrange the dividend and divisor so that the dividend contains two more decimal places than the divisor. This may be done by annexing ciphers to one or the other of these terms, as may be necessary. If the quotient is not exact when two decimal places have been reached, express the remainder as a common fraction, in the quotient, thus: a. 7 bushels are what per cent of 8.5 bushels? b. A lake in Maine is 152.875 rods long and 92 rods wide. Its length is what per cent of its width? NOTE. Care should be taken to express the decimal rate per cent properly, as hundredths. Every fractional part of 1% must be written at the right of the hundredths' place. 3. 35% of a number is 700. Find the number. 4. 84.20 is what per cent of 421 ? 5. Find % of $5600. 6. Find 66% of 927 tons. 7. 39.744 is what per cent of 900 ? 8. A short ton is what per cent of a long ton? 9. 386% of 244 what? 10. 231% of a number is 7000. Find the number. 11. A nautical mile is 6086.07 feet. A statute mile is what per cent of a nautical mile? 12. Find a number, 7 per cent of which is 287. 13. 48 rods are what per cent of a mile? 14. 57 cubic inches are what per cent of one gallon ? 15. Find 3% of $235. 16. 17% of 2475 is what per cent of 720? 18. A man's salary is $1850 and his expenses $1757.50. His expenses are what per cent of his salary? 19. A man's expenses are $2140 a year. His salary is 125% of this sum. Find his salary. 20. A man bequeathed 18% of his estate to a hospital, 7% to a missionary society, and 30% to his wife. The remainder was divided equally among his three brothers. If the estate amounted to $72,600, how much did each of the brothers receive? 21. For how much a month must a house worth $6000 be rented in order that the rent may amount to 7% of the value of the house? 22. A grocer bought 12 cases of coffee, each containing 50. one-pound packages, and sold 240 packages. What per cent of the coffee did he sell? 23. Which is greater, and how much, 50% of 75, or 75% of 50? 24. A field is 375 feet long and 150 feet wide. a. Its breadth is what per cent of its length? b. Its length is what per cent of its breadth? 25. Find in acres the area of a rectangular field whose width is 45 rods and whose length is 1423% of its width. 26. A manufacturing company employing 272 persons, whose weekly wages average $12 apiece, raises the wages of its employees 81%. How much per year is then paid to all of them? 27. 18% of the men in an army died of disease. If the loss from this cause was 1260 men, how many men were there in the army at first? 28. A man having $20,000 in the bank drew out 30% of it and then 25% of what was left. How many dollars still remained in the bank? 29. 83% of the boys in a military school attended a game of football. If 166 boys attended the game, how many boys were there in the school? PER CENTS EQUIVALENT TO COMMON FRACTIONS 260. All percentage problems involving the relation of product and factors may be solved in decimals. But in many cases the work may be shortened by changing the per cents to common fractions. 261. Oral 1. The whole of anything is how many hundredths of it? What per cent of it? 20 2. of anything is how many hundredths of it? ? ? 16? q? q? q? #? 1? #? %? J? }? ?? ? ? 12? 26? 3. What common fraction is the same as .10? .20? .30? .40? .50? .60? .70? .80? .90? .25? .331? .14? 621? .371? .66? .121? .871? .75? .163? .831? .08 .05? 4. What per cent is the same as 1? 1? 11⁄2? 1? 1? ? ? ? ? ? ? ? ? ? 쑴? 응? 흉? ?? 6. What per cent of anything is left after 50% of it has been taken away? After 75% of it has been taken away? 30%? 40%? 35%? 331%? 621%? 371%? 831%? 16%? 49%? 1%? 21%? 981%? 7. What per cent of anything is left after 15%, 10%, and 5% of it have been taken away? 8. A girl used 12% of her Christmas money on one day, 18% the next day, and 15% the next day. What per cent of her money remained? 9. 97 per cent of the pupils belonging to a certain school were present. What per cent of the pupils were absent? 10. 23% of the pupils in a school were absent. cent of the pupils were present? What per |