Vanessa purchased a smart TV for $1,500 on a payment plan. Four months after purchasing the TV, her balance was $1,200. 7 months

Question

3 years ago

7

Vanessa purchased a smart TV for $1,500 on a payment plan. Four months after purchasing the TV, her balance was $1,200. 7 months

after purchasing the TV, her balance was $975. Find an equation that models the balance B(t) after t months. How many months will it take her to pay off the TV loan?

Mathematics

1 answer:

Vedmedyk [2.9K] · Answer 1 · 2022-05-20T10:45:23+03:00

Answer:

B(t) = 1500 - 75(t)

It will take her 20 months to pay off her debt.

Step-by-step explanation:

Vanessa purchased a smart TV for $1500 on a payment plan. 4 months after purchasing the TV her balance was $1200. This means for the 4 months period she paid $300 . This simply translate to her paying $75 each month for the 4 month duration.

7 months after her balance was $975 . For 7 months duration her balance was $975 which simply means she paid 7 × 75 = $525 during the 7 months period.

The equation to model the balance B(t) after t months can be represented below.

Each month she pays $75 to dislodge her debt. For t months her balance will be

B(t) = 1500 - 75(t)

The number of month it will take her to pay off her loan means her balance will be $0.

B(t) = 1500 - 75(t)

-1500 = -75t

t = -1500/-75

t = 20

It will take her 20 months to pay off her debt.