Solving a Percent Equation with an Unknown Base Example 3 Section 2.5 Applications Involving Percents 159 Andrea spends 20% of her monthly paycheck on rent each month. If her rent payment is $950, what is her monthly paycheck? Solution: Step 1: Read the problem. Let x represent the amount of Step 2: Label the unknown. Andrea’s monthly paycheck. The problem can be rephrased as: $950 is 20% of what number? Step 3: Write a verbal model. x 950 0.20 Step 4: Write a mathematical equation. Step 5: Solve the equation. Divide both sides by 0.20. 950 0.20x 950 0.20 0.20x 0.20 4750 x Andrea’s monthly paycheck is $4750. Step 6: Interpret the results. 2. Applications Involving Simple Interest One important application of percents is in computing simple interest on a loan or on an investment. Simple interest is interest that is earned on principal (the original amount of money). The following formula is used to compute simple interest: a in yearsb annual a Simple b aprincipalb b interestinterest rateThis formula is often written symbolically as I Prt. a time For example, to find the simple interest earned on $2000 invested at 7.5% interest for 3 years, we have I P r t Interest 1$2000210.0752132 $450 Applying Simple Interest Example 4 Jorge wants to save money to buy a car in 5 years. If Jorge needs to have $20,250 at the end of 5 years, how much money would he need to invest in a certificate of deposit (CD) at a 2.5% interest rate? Solution: Step 1: Read the problem. Let P represent the original amount invested. Step 2: Label the unknown. Skill Practice 4. In order to pass an exam, a student must answer 70% of the questions correctly. If answering 42 questions correctly results in a 70% score, how many questions are on the test? Classroom Example: p. 162, Exercise 24 Skill Practice 5. Cassandra invested some money in her bank account, and after 10 years at 4% simple interest, it has grown to $7700. What was the initial amount invested? Classroom Example: p. 162, Exercise 28 Answers 4. There are 60 questions on the test. 5. The initial investment was $5500.
miller_introductory_algebra_3e_ch1_3
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