2. a. When the base and the percentage are known, how is the rate found? What is the formula? b. When the rate and the base are known, how is the percentage found? What is the formula? c. When the percentage and the rate are known, how is the base found? What is the formula? 3. Find the percentage when the base is $378.45 and the rate 331%• 4. Find the base when the rate is 6% and the percentage is $426.24. 5. Find the rate when the base is $372.40 and the percentage is $409.64. 6. Write as a decimal: %; 31%; 225%; 350%. 8. Find 350% of $274. 9. A dime is what per cent of $2.00? of $5.00? of $10.00? 10. a. What is meant by increasing a number? b. What is meant by decreasing a number? c. How many per cent of a number is that number increased by 18% of itself? d. How many per cent of a number is that number decreased by 74% of itself? 11. A man whose salary was $5000 a year was given a bonus of $1000 at Christmas time. How many per cent of his salary was this? 12. A man paid $115.25 in taxes last year. He was told that taxes would increase about 6% this year. What would his taxes be, approximately? 13. A contractor estimated that the cost of building houses had increased about 60% in the past five years. What would it cost now to build a house that had cost $6300 five years before? 14. 40 rods is what per cent of a mile? 15. One square foot is what per cent of a square yard? 16. What number increased by 5% of itself is $971.25? 17. What number decreased by 18% of itself is $305.04? 18. A yard is what per cent of a foot? 19. A gallon is what per cent of a quart? 20. A bushel is what per cent of a peck? 21. a. A dry goods merchant advertised a discount of 334% on certain shopworn table linen. What would be the sale price of a tablecloth marked $6.45? b. What is meant by a discount? c. Tell two reasons why discounts are given by merchants. 22. Out of a salary of $2250 per year a man spends $112.50 for life insurance. What per cent of his salary is spent for life insurance? 23. Out of eight games played by a football team, the team won five. What per cent did it win and what per cent did it lose? 24. Another team won four games out of seven that it played. How does the per cent of games it won compare with the per cent won by the team in Example 23? 25. A man received $225 per acre for a farm that cost him $200 per acre. What per cent of the cost was his profit? 26. In one class, 14 pupils out of 28 were marked excellent; in another, 4 out of 24 were marked excellent. Find the per cent of each class marked excellent. 27. Find R when P = $917.00 and B = $3275. 28. Find P when R=621% and B = $74.64. 29. Find B when P=435 and R = 15%. 30. A woman's hat cost $5.00. It was marked for sale at a gross profit of 200% of the cost. At the close of the season it was sold at a discount of 50% of the marked price. What was the gross profit on the hat after the discount? 31. A suit that cost the dealer $28.50 was marked to sell at an advance of 40% of the cost. At the end of the season, the suit was sold at a discount of 15% from the marked price. What was the final sale price? What was the gross profit on the suit if sold at the sale price? 32. If the pay a man receives now is more than that he received a year ago, how do you find what per cent of hist former pay his increase is? 33. If you know the cost of an article and the selling price of it, tell how to find what per cent of the cost the gross profit is. Tell also how to find what per cent of the selling price the gross profit is. 34. If you know the selling price of an article, and know that the gross profit is a certain per cent of the selling price, how can you find the gross profit? How can you find the cost? 35. If a man knows how many tons of coal he burned, and how many pounds of ashes he has in his ash pile: a. How can he find how many tons of ashes he has? b. How can he find what per cent of his coal was ashes? VII. INTEREST 43. Interest is money paid for the use of money. It is like rent paid for the use of a house, or farm, or automobile. The amount of rent that one pays for a house or a farm depends upon the value of the property and upon the length of time that the property is rented. Similarly, the amount of interest paid for the use of money depends upon the amount of money borrowed and upon the length of time that it is borrowed. Thus a man can borrow $100 from a bank and keep it for a whole year by paying $6 interest. If he keeps it for two years, he will have to pay 2 times $6 or $12; if he keeps it for only one half a year, he will pay one half of $6 or $3. If he borrows $200 for one year, he will pay 2 times $6 or $12. For every $100 that he borrows he will have to pay $6 interest. Notice that he pays 6% of the amount he borrows, if he keeps it one year. The money borrowed is called the principal. The interest for one year is a certain rate per cent of the principal; this rate is called the rate of interest. The year is regarded as consisting of twelve months of thirty days each, or of 360 days; this practice makes interest computation easier. The sum of the principal and interest is called the amount. 44. General method of computing interest. Example 1. A man borrows $2000 for 3 years, agree. ing to pay 6% interest annually. How much interest is due at the end of 3 years? What is the amount due then? Solution. 2. 3. 1. The interest for 1 year = 6% of $2000 = $120. The interest for 3 years =3×$120 = $360. The amount in 3 years = $2000 +$360 = $2360. If the time had been one and one half years, the interest would have been 3×$120 or $180. Rule. To find the interest on any principal for a given length of time, at a given rate of interest, multiply the principal by the rate, and that result by the number of years in the time. EXERCISE 57 Find the interest to be paid: 1. On $500 borrowed for 1 year at 6% per year. year at 6% per year. years at 6% per year. years at 5% per year. year at 8% per year. years at 4% per year. Find the interest and the amount to be paid: years at 5% per year. year at 6% per year. 8. On $975 borrowed for 3 9. On $625 borrowed for 10. On $1200 borrowed for 14 years at 8% per year. 11. On $275 borrowed for 6 months at 5% per year. 12. On $1500 borrowed for 4 months at 4% per year. 13. On $1500 borrowed for 3 months at 5% per year. 14. On $375.50 borrowed for 9 months at 6% per year 15. On $85 borrowed for 3 months at 8% per year. |