Question

Zachary purchased a computer for ​$1,100 on a payment plan. Two months after he purchased the​ computer, his balance was ​$870. Six months after he purchased the​ computer, his balance was ​$410. What is an equation that models the balance y after x​ months?

Answer 1

y = 1100 - 115x

Explanation:

Let the monthly payment be $p

In two months Zach would have paid 2p dollars

Balance would be 1100 - 2p = y

We know after 2 months, balance y was actually 870

Substituting y = 870 we get
1100 - 2p = 870

Subtract 1100 on both sides

1100 - 1100 - 2p = 870 -1100

==> -2p = - 230

Divide by -2 on both sides

-2p/-2 = -230/-2

p = 115 which represents the monthly payment .

So the balance y after m months is given by the equation
y = 1100 - 115x

We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent