154 Chapter 2 Linear Equations and Inequalities in One Variable 1d. In fall 2000, enrollment in public preK–12th grade nationwide was 47.2 million. In fall 2010, the enrollment in preK–12th grade was 50 million. What was the percent increase in enrollment from 2000 to 2010? Solution 1d. What is unknown? The percent increase in enrollment between 2000 and 2010 is unknown. Let x = percent increase in enrollment in schools. What is known? The original enrollment (in 2000) was 47.2 million. The new enrollment (in 2010) was 50.0 million. To solve this problem, we use the following relationship. Percent increase or decrease = new amount - original amount original amount x = 50 - 47.2 47.2 x = 2.8 47.2 x ≈ 0.059 Replace the new amount with 50 and the original amount with 47.2. Simplify the numerator. Divide. So, the enrollment increased by 5.9% from fall 2000 to fall 2010. Student Check 1 Write an equation that represents each situation. Solve the equation and answer the question in a complete sentence. a. Using the percentages from Oprah’s Debt Diet, what is a family’s monthly income if they spend $450 on transportation each month? b. A shirt is on sale for $21. This is 30% off the original price. What is the original selling price of the shirt? c. Aisha’s salary after her raise is $55,640. Prior to the raise, her salary was $52,000. What percent raise did she receive? d. The national debt was $10.6 trillion on the day President Obama took office. The Obama Administration’s 4-year estimate shows that by the end of September 2012, the debt will reach $16.2 trillion. What is the projected percent increase in the national debt from 2009 to 2012? (Source: http://www.cbsnews.com/blogs/2009/03/17/politics/politicalhotsheet/ entry4872310.shtml) Simple Interest Problems Interest is the amount of money collected for investing or borrowing money. Banks pay its customers interest when they invest money into their bank. Customers pay banks interest when they borrow money from the bank. One type of interest is simple interest. Simple interest is interest earned on the amount that was initially invested or borrowed. Simple interest is computed as follows. �������������������� Simple Interest Formula Interest = principal × rate × time or I = prt Principal, p, is the amount initially invested or borrowed. Rate, r, is the annual interest rate (must be converted to a decimal). Time, t, is the years that the money was invested or borrowed. Objective 2 ▶ Solve simple interest applications.
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