How many dollars was Don's down payment?

Question

y=90x+75

 

Don bought a sofa with 0% interest for the 1st 36 months. He makes a small down payment, and then he makes equal monthly payments until he pays off the sofa. The above equation models the number of payments, x, that he makes to pay for a sofa that costs y dollars. How many dollars was Don's down payment?

Answer 1

If y represents the total cost of the sofa and Don pays in full for the sofa with a combination of a down payment and a series of monthly payments, then the total cost of the sofa must equal the sum of:

- the value of each monthly payment multiplied by the number of payments (x) PLUS

- the value of the down payment.

 

Therefore Don's monthly payment must be $90 (so that the total amount paid towards the cost of the sofa via monthly payments is equal to 90 * x). The remaining cost of the sofa is paid by Don's down payment, which must be equal to the remaining portion of the equation, $75.