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

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

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 = (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.