Section 2.6 Percent, Rate, and Mixture Problems 151 122. The supplement of an angle is 14° less than six times its complement. Calculate the measure of the angle. Francis’ work: 180 - x = 14 - 6(x - 90) 180 - x = 14 - 6x + 540 5x = 374 x = 74.8 Calculate It! Solve each equation. Then use a graphing calculator to check the answer. 123. 0.03(x + 5.4) = 0.02(x - 1.8) + x 124. 180 - x = 5(90 - x) - 24.8 125. 5x - 32.6 + 3(x + 4.2) = 180 126. The formula to find the volume of a cylinder with radius r and height h is V = πr2h. Use π = 3.14 to find V if r = 15.6 ft and h = 6.5 ft. �� ������������������������ Percent, Rate, and Mixture Problems According to Oprah’s Debt Diet, how a family should spend their monthly income is based on this pie chart. Because the pie chart illustrates how a family should allocate all of their monthly income, the percents add to 100%. If a family following this “diet” spends $1400 on housing each month, what is their monthly income? (Source: www.oprah.com) We will learn how to solve this problem using a linear equation. Transportation 15% Percent Applications Many real-life situations involve percents—paying taxes, sale discounts, investments, commissions, and so on. In this section, we will explore applications of linear equations involving percents. Recall that percent means per hundred. For example, 5% = 5 100 = 0.05. Percents can be converted to decimals by dropping the percent sign and moving the decimal two places to the left. Following are four specific types of applications of percents. ���������������� General Percent Problem An example of a general percent problem is to answer the question “30 is 15% of what number?” To answer this question, we let n represent the unknown number. Recall that 15% of a number is equivalent to multiplying the number by 0.15. So, we have that 30 = 0.15n 30 0.15 = 0.15n 0.15 200 = n The number is 200. ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Solve percent applications. 2. Solve simple interest applications. 3. Solve mixture applications. 4. Solve distance, rate, and time applications. 5. Troubleshoot common errors. Objective 1 ▶ Solve percent applications. Housing 35% Debt 15% Other Living Expenses 25% Savings 10%
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