Question

Diane owes $20125.00 to the bank after completing her college degree. With the funds from her new job she is paying back $144.00 per month. Her friend Teresa was given $16835.60 in the bank for college from her family, and she is spending $394.00 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

Diane will have the same bank balance as Teresa after approximately 2.2 months.

Step-by-step explanation:

To find out after how many months Diane will have the same bank balance as Teresa, we need to set up a function for each person's bank balance.

Let's call the number of months x. For Diane, her bank balance can be represented by the function:

Bank balance of Diane = $20,125 - $144x

And for Teresa, her bank balance can be represented by the function:

Bank balance of Teresa = $16,835.60 - $394x

We need to find the value of x when the bank balances of both Diane and Teresa are equal. In other words, we need to solve the equation:

$20,125 - $144x = $16,835.60 - $394x

Simplifying this equation, we get:

$558 = $250x

Dividing both sides by $250, we get:

x = 2.232

Rounded to the nearest tenth, Diane will have the same bank balance as Teresa after approximately 2.2 months.