CPM Homework Help : AC Problem 9-55

Zachary has $$718$ in his bank account and automatically withdraws (subtracts) $$14$ every month to pay for his computer service. Christian has $$212$ in his bank account and deposits (adds) $$32$ each month from his newspaper delivery tips. Assuming they make no other deposits or withdrawals, when will Zachary and Christian have the same amount of money in their bank accounts?

Hint:

Create a system of equations that represents the problem.

Step 1:

Define your variables.

$y =$ total amount of money in the account
$x =$ number of months

Step 2:

$\begin{array}{l} y = -14x + 718 \\ y = 32x + 212 \end{array}$

Step 3:

Set the equations equal to each other and solve for $x$ .

$\begin{array}{c} -14x + 718 = 32x + 212 \\ \quad 506 = 46x \end{array}$

Answer:

After $11$ months they will have the same balance.

$11 = x$