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?

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:[tex]y_l = 10000 - 250x[/tex]Value of the car after x months:[tex]y_c = 8000 - 50x[/tex]Which statement describes when Melinda’s loan will be equal to the value of the car?They are equal when:[tex]y_l = y_c[/tex]So[tex]10000 - 250x = 8000 - 50x[/tex][tex]200x = 2000[/tex][tex]x = \frac{2000}{200}[/tex][tex]x = 10[/tex]Equal after 10 months:Value of [tex]y(10) = 8000 - 50(10) = 7500[/tex]Thus, the correct option is:After 10 months, the loan and value of the car will both be equal to $7,500.