A local bank recommends opening a savings account with a $100 initial deposit and a $15 monthly deposit. A local credit union recommends opening a savings account with a $50 initial deposit and a $20 monthly deposit. A system of equations is written to find the month at which the two accounts have the same balance. If x represents the number of months after the initial deposit and y represents the account balance in dollars, the equation for the credit union account balance is y = 20x + 50. What is the equation for the bank account balance?

Answer 1

To find the equation for the bank account balance, we need to consider both the initial deposit and the ongoing monthly deposits.

1. The bank account has an initial deposit of $100.
2. It also has a monthly deposit of $15.

Let \( x \) represent the number of months after the initial deposit, and \( y \) represent the account balance in dollars.

The equation for the bank account balance, taking into account the initial deposit and the monthly deposits, can be written as:

\[ y = 15x + 100 \]

Here, \( 15x \) represents the total amount deposited over \( x \) months, and \( 100 \) is the initial deposit.