Step 3: Write a verbal model. Step 4: Write a mathematical equation. Step 5: Solve the equation. 160 Chapter 2 Linear Equations and Inequalities a Original b 1interest2 principal 1total2 P Prt total P P10.0252152 20,250 P 0.125P 20,250 1.125P 20,250 1.125P 1.125 20,250 1.125 P 18,000 The original investment should be $18,000. Step 6: Interpret the results and write the answer in words. 3. Applications Involving Discount and Markup Applications involving percent increase and percent decrease are abundant in many real-world settings. Sales tax for example is essentially a markup by a state or local government. It is important to understand that percent increase or decrease is always computed on the original amount given. In Example 5, we illustrate an example of percent decrease in an application where merchandise is discounted. Applying Percents to a Discount Problem Example 5 After a 38% discount, a used treadmill costs $868 on e-Bay. What was the original cost of the treadmill? Solution: Step 1: Read the problem. Let x be the original cost of Step 2: Label the unknown. the treadmill. Step 3: Write a verbal model. a Original b 1discount2 b cost pricex 1x2 a sale 0.38 868 Step 4: Write a mathematical equation. The discount is a percent of the original amount. Step 5: Solve the equation. Combine like terms. Divide by 0.62. x 0.38x 868 0.62x 868 0.62x 0.62 868 0.62 x 1400 The original cost of the treadmill Step 6: Interpret the result. was $1400. Avoiding Mistakes The interest is computed on the original principal, P, not on the total amount $20,250. That is, the interest is P (0.025)(5), not ($20,250)(0.025)(5). Skill Practice 6. An iPod is on sale for $151.20. This is after a 20% discount. What was the original cost of the iPod? Classroom Example: p. 162, Exercise 36 Answer 6. The iPod originally cost $189.
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