Question

Diane owes $10097.00 to the bank after completing her college degree. With the funds from her new job she is paying back $158.00 per month. Her friend Teresa was given $7525.90 in the bank for college from her family, and she is spending $391.00 per month out of this college fund. If these were continuous functions, after how many months will Diane have the same bank balance than Teresa, rounded to the nearest tenth?

Answer 1

By setting up an equation to solve for the number of months in which Diane's decreasing debt is equal to Teresa's depleting funds, we find that after approximately 11.0 months, they will have the same bank balance.

Step-by-step explanation:

To find out after how many months Diane will have the same bank balance as Teresa, we can set up an equation where the decreasing debt of Diane and the depleting funds of Teresa are equal. Let's denote the number of months as m.

Diane starts with a debt of $10,097 and pays off $158 per month. Therefore, her debt after m months is $10,097 - $158m.

Teresa starts with a college fund of $7,525.90 and spends $391 per month. Therefore, Teresa's remaining fund after m months is $7,525.90 - $391m.

To find out when they will have the same balance, we set up the equation:

$10,097 - $158m = $7,525.90 - $391m

By combining like terms and solving for m, we get:

$2,571.10 = $233m

m = $2,571.10 / $233 ≈ 11.0 months

Therefore, after approximately 11 months, Diane will have the same bank balance as Teresa.