Melinda takes out a loan to purchase a car. The balance on her loan after x months is represented by the equation y = 10,000 – 250x and the value of the car after x months is represented by y = 8,000 – 50x. Which statement describes when Melinda’s loan will be equal to the value of the car?

Set the loan balance equal to the car’s value: 10,000 − 250x = 8,000 − 50x. Solving gives 2,000 = 200x, so x = 10 months. At 10 months, both amounts are $7,500, so the correct statement is that after 10 months the loan and car value will both be $7,500.

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