FINDING THE RATE 327. Reasons for Finding the Rate. It is frequently important to know how many per cent one number is of another. Thus, in a census it is found that a state with a population of 2,649,260 has 78,240 illiterates; while in another state with a population of 678,925 there are 23,284 illiterates. To decide which state has the greater proportion of illiterates, we find how many per cent of each population are illiterate. 328. Rule for Finding the Rate. Example 1. 16 is how many per cent of 400 ? Example 2. 24 is how many per cent of 270? Solution. 8.89 2.7)240 216 240 in 24. 216 240 Analysis: 1% of 270 = 2.70. 2.70 is contained 8.89 times Rule: To find the rate per cent, divide the percentage by one per cent of the base. Find the rate to the nearest tenth of one per cent. 329. Applications of Finding the Rate. The table below gives the number of persons in the United States over 10 years of age, and the number of illiterate persons in each class in 1910. Supply the missing per cents in this table. Notice how the per cents enable you to compare the illiteracy of the different classes of people. POPULATION 10 YEARS OF AGE AND OVER - 1910 FINDING THE BASE 330. Example. If a certain grade of milk contains 4% of butter fat, how many pounds of milk must be delivered to a creamery to furnish 650 pounds of butter fat? Analysis: Since 4% of the milk equals 650 pounds, of 650 lb., or 162.5 lb., equals 1 per cent of the required amount. Hence 100 × 162.5 = 16250 is the number of pounds required. Solution. 16250. .04)650.00 To simplify the work we divide by .04 instead of dividing by 4, and then multiplying by 100. Rule: To find the base, express the rate as a decimal and divide the percentage by it. WRITTEN EXERCISES Find the base accurate to two decimal places in each of the follow 331. Finding the Base when Rate is an Aliquot Part of 100. When the rate is an aliquot part of 100 the base can be found as in the following: Example 1. 16 is 20 % of what number? Solution. 20% = . Hence the base is 5 X 16 = 80. Example 2. 240 is 33% of what number? == 720. 1. A certain grade of fine gunpowder contains 75% niter, 15% charcoal, and 10% sulphur. How much gunpowder can be made by using 15 tons of niter? 2. A certain grade of Tungsten steel contains 9.3% of Tungsten. How many tons of such steel can be made, using one ton of Tungsten ? 3. A certain grade of nickel steel contains 27% of nickel. How many tons of such steel can be made, using 45 tons of nickel? 4. A certain grade of Babbitt's metal (used in bearings on railway cars, etc.) contains 88.9% tin, 3.7% copper, and 7.4% antimony. How much copper is required for an order of 25 tons of this metal? 5. How many tons of Babbitt's metal can be made, using 1 ton of copper? 6. How many tons of Babbitt's metal can be made, using 20 tons of tin? 7. How many tons of Babbitt's metal can be made, using 1 ton of antimony? Problems of the kind shown in the two examples on this page are of frequent occurrence. Example 1. What number increased by 25% of itself equals 1740 ? Analysis: (a) The required number equals 100 of itself. Hence 1730 = 125% of the required number and hence the required number is 1740 ÷ 1.25 = 1392. 1392 = (b) 1740 125% of the required number or of it. Hence of 1740 348 = of the required number, and 4 X 348 the required number. = = = *1392 = Example 2. What number decreased by 15% of itself equals 1. What number increased by 5% of itself is equal to 378? 2. What number increased by 30% of itself is equal to 1625? 3. Having increased my capital by 12% of itself, I find that I have $380,000. How much had I at first? 4. My crop of oats this year is 15% greater than my crop last year and during the two years I raised 5375 bushels. What was my last year's crop? 5. What number diminished by 5% of itself is equal to 380? 6. What number diminished by 20% of itself is equal to 1008? 7. A merchant received 80% of a consignment of grain; he sold 20% of what he received and then found that he had left 576 bushels. What was the entire consignment? |