Answer 8. The Craftsman model costs $190 and the DeWalt model costs $500. Applying a Linear Equation 42– Example 6 One model of a HDTV sells for $800 more than a smaller 32– HDTV. The combined cost for these two televisions is $2000. Find the cost for each television. 164 Chapter 3 Solving Equations Solution: Step 1: Read the problem completely. Let x represent the cost of the TV. Step 2: Label the unknowns. Then x 800 represents the cost of the TV. Step 3: Write an equation in words. 42– Cost of 32– b a cost of 42– 32– b a total cost b x x 800 2000 Step 4: Write a mathematical equation. Step 5: Solve the equation. Combine like terms. Subtract 800 from both sides. Divide both sides by 2. Step 6: Interpret the results in words. x x 800 2000 2x 800 2000 2x 800 800 2000 800 32– 2x 1200 2x 2 1200 2 x 600 a Since x 600, the TV costs $600. The cost of the 42– model is represented by x 800 $600 $800 $1400. TIP: In Example 6, we could have let x represent either the cost of the TV or the TV. Suppose we had let x represent the cost of the 42– model. Then x 800 is the cost of the model (the model is less expensive). x 800 x 2000 2x 800 2000 2x 800 800 2000 800 2x 2800 Therefore, the 42– TV costs $1400 as expected. The 32– TV costs x 800 or $1400 $800 $600. x 1400 a Cost of 32– b a cost of 42– b a total cost b 32– 32– 42– 32– Skill Practice 8. A kit of cordless 18-volt tools made by Craftsman cost $310 less than a similar kit made by DeWalt. The combined cost for both models is $690. Find the cost for each model. (Source: Consumer Reports)
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