3. The following poster was displayed in the waiting room of a railroad station: WHAT HAS HAPPENED TO THE RAILROADS SINCE 1916? Increase in revenue Increase in expenses 60% 110% What is your answer to the question? 144. To change per cent to a decimal fraction. We have seen (p. 31) that in everyday life measures are frequently expressed as per cent, and that per cent means in hundredths. In other words, 88 per cent is the same as, or as .88. This shows that per cent may always be expressed as a decimal by dividing the number of per cent by 100. 145. To express per cent as a common fraction. We have seen that 88% means the same as 100. 88 Thus, per cent may be expressed as a common fraction by dividing the number of per cent by 100 and then reducing the resulting fraction to lowest terms. EXERCISES Express per cents as common fractions to lowest terms, as shown above: 146. Summary of important per cents expressed as decimals and as common fractions. Certain per cents are so commonly used that they should be memorized. Write into your notebook a complete table like the one 147. Percentage. Base. We have seen that 75% of a number means .75 of it, or of it. Hence, 75% of 360 means .75×360, or of 360. The 360 in this example is the base, and .75×360 is the percentage. In other words, the number of which a per cent is taken is called the base, and the result obtained by taking a per cent of a number is called the percentage. If the percentage is denoted by p, the number of per cent by r, and the base by b, the statement percentage is equal to the rate per cent multiplied by the base takes the simple form This is the percentage formula. It may be used to find any one of the three literal numbers p, r, and b, if the other two are known. EXERCISES Using the percentage formula, find the percentage p in each of the following exercises and problems as shown in the solutions of Exercise 1. 1. 25% of 48. Since r=25 and b=48, we may substitute these values in the formula 20. In a school of 560 pupils, 50% are boys. How many boys are there? 21. A man saves 163% of his income. If his income is $2400, how much does he save? 22. A girl earning $18 a week plans to use 20% of her income for clothing. How much money must she set aside for clothing during one year? 23. Many families plan in advance the expenditures for each month. A certain amount is set aside for rent, another car fare, 15%; for recreation, books and papers, church, education, doctor, dentist, insurance, and savings, 25%. Make out a budget showing how much money a family can spend for the various items above, if the income is $3600. Tabulate the amounts as shown below: Income Food Rent Clothing Current Health, Recreation, Etc. 24. A man bought a house for $6200 and sold it with a gain of 15% on the purchase price. How much did he gain? 25. An automobile purchased for $1650 is sold at a reduction of 25%. What was the selling price? 26. A manufacturer announces a 10% bonus for all employees. If a man's salary is $2200, how large a bonus is he going to receive? |