Question

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?

After 10 months, the loan and value of the car will both be equal to $7,500.
After 12 months, the loan and value of the car will both be equal to $7,000.
After 14 months, the loan and value of the car will both be equal to $6,500.
After 16 months, the loan and value of the car will both be equal to $6,000.

Answer 1

Set the expressions equal: 10,000 − 250x = 8,000 − 50x.
Solve: 2,000 = 200x → x = 10.
At x = 10 months both equal 10,000 − 2,500 = $7,500.

So the first statement is correct.