Vanessa purchased a smart TV for

$1,500 on a payment plan. Four

months after purchasing the TV, her

balance was $1,200. Seven months

after purchasing the TV, her

balance was $975. Find an equation

that models the balance y after t

months. How many months will it

take her to pay off the TV loan?

y = 1500 - 75t

It will take her 20 months to pay off her TV loan.

Step-by-step explanation:

Vanessa purchased a smart TV for $1500 on a payment plan. After 4 months of purchasing the TV her balance was $1200. 7 month her balance was $975. The amount she pays every month can be calculated as follows. After 4 months she paid 1500 - 1200 = $300. Her balance is $1200. Divide 300 by 4 to get $75 per month as the amount she pays every month.

1500 - 975 = 525/7 = $75 per month.

The equation to model the balance y after t months can be expressed below.

y = 1500 - 75t

where

y = balance

t = number of months

Her balance should be $0 for her to be able to pay off the TV loan.

y = 0

-1500 = - 75t

divide both sides by - 75

t = - 1500/-75

t = 20

It will take her 20 months to pay off her TV loan.