23. An architect was paid 5% of the cost of a house for drawing the plans and supervising the building of it. If the house cost $11,760, how much did he receive as his fee? 24. Some realtors charge 3% of the value of a house for selling it. My house was sold for $8250. How much did the realtor receive for making the sale? 25. In a high school which had 450 boys, 8% of them tried for the baseball team. How many tried? Finding Percentage by Algebraic Formula. — We usually call per cent rate per cent, or simply rate, or fractional part. The number of which we find the per cent is called the base or whole. The result of our work is called percentage or part. We must get clearly in mind the difference between per cent and percentage. Per cent is the rate; percentage is the result or part. Illustrative Example. Find 8% of $160. Solution: 8% of $160.08 × $160 rate = $12.80. base percentage We have, therefore, the following rule: To find the percentage, multiply the base by the rate. = Or more simply percentage base X rate. If we use only the initial letters of the words, we have p = b xr, or written algebraically p = br. This is the formula for percentage. Algebra Helps Arithmetic Do Your Work In the following examples use the above formula to find the percentage. Everyday Problems in Percentage Estimate your answers, writing the estimates in a vertical column. When you have completed your estimates, work the problems on paper. Compare your answers with your estimates by writing the answers in a second vertical column. In cases where estimates and answers differ to a large extent, check by working the problem again. What proportion of sensible estimates can you make? 1. A man receiving a yearly salary of $3600 saved 20% of it. How much did he save? 2. John had 60 cents in the morning. He spent 15% of it during the day. How much did he spend? How much had he left? 3. Find the value of 36% of 2000 bushels of wheat at $1.15 a bushel. 4. What is the value of 75% of 256 acres of land at $56 an acre? 5. The depreciation (loss of value) of a new automobile is computed at about 30% of its original value for the first year. If an automobile costs $1400 when new, what is its value at the end of the first year? 6. If the same automobile loses 18% of its cost during the second year, what is it worth at the end of the second year? 7. If the automobile cost the owner 4% of its cost to insure it against fire, theft, liability, property damage, and collision, how much insurance cost would he have to pay the first year? 8. Mr. Jones is worth 48% of $50,000 and Mr. Noble is worth 56% of $40,000. Which is worth the more and how much? 9. A suit of clothes was marked $40. During a sale the merchant reduced it 15%. How much did he reduce it? What was the new sale price? 10. If I borrow $3000 to help pay for a house and am charged 6% a year for the use of the money, how much must I pay annually for the use of it? 11. There were 3600 people in attendance at a county fair one day. The next day on account of rain the attendance was 42% less. How many attended the second day? 12. Mr. Howard, whose income is $2500, spends 20% of it for rent, 25% of it for food, 15% for fuel and light, 15% for clothing, 10% for car fare, and the balance for savings. How much does he save? 13. Oakland, California, had about 216,300 inhabitants in 1920. If by 1925 the population had increased 12%, how much had it increased in the five years? What would be the new population? 14. Mary was working for $16 a week but on account of poor business her employer told her he would have to reduce her salary 12%. How much was she reduced per week? What was her new salary? 15. A clerk was paid 3% of the amount of the goods that he sold. On a certain day he sold $340.50 worth of goods. How much did he earn that day? More Even Exchange. Business men often change per cents to common fractions by writing 100 as the denominator and reducing to lowest terms. Illustrative Example 1. What common fraction is equivalent to 5%? Solution: In order to solve this we write Illustrative Example 2. Change 33% to a common fraction. What did we do to both the numerator and the denomi nator when we changed from 331 100 ? to 100 300 Illustrative Example 3. What is the equivalent common fraction for %? Keeping the Change Correct I. R. B. Test [1]. Prepare in I. R. B. a chart for the First, End-of-Chapter, Review, and Fourth Trial records (seven tests). Record your first score in the proper column. Have the Steering Committee determine the standard time. Keep your time and accuracy score. Change each of the following per cents to fractions in their lowest terms or to mixed numbers. See if you can do all of them mentally. 1. 20%. 6. 45%. 2. 25%. 7. 80%. 8. 95%9. 75%. 11. 66%. 16. 83% 21. 125%. 22. 375% 3. 4%. 4. 6%. 14. 16%. 19. 250%. 24. 1%. 5. 30%. 10. 37%. 15. 24%. 20. 400%. 25. 1%. Table of Equivalents. "Have the Exact Change Ready." Most business men know the per cent equivalents for the most commonly used fractions. The following table contains some important fractions expressed as per cents. You should memorize them. To help your memory, copy the fractions in your I. R. B., and then write the equivalents without referring to the book. Review Aliquot Parts on page 36. |