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

Answer:

After 10 months, the loan and value of the car will both be equal to $7,500.

Step-by-step explanation:

Value of the loan after x months:

$y_l = 10000 - 250x$

Value of the car after x months:

$y_c = 8000 - 50x$

Which statement describes when Melinda’s loan will be equal to the value of the car?

They are equal when:

$y_l = y_c$

So

$10000 - 250x = 8000 - 50x$

$200x = 2000$

$x = \frac{2000}{200}$

$x = 10$

Equal after 10 months:

Value of $y(10) = 8000 - 50(10) = 7500$

Thus, the correct option is:

After 10 months, the loan and value of the car will both be equal to $7,500.