3.

Question

In February, you have a balance of $270 in your bank account. Each month you deposit $45. Let January = 1, February = 2, and so on. Write an equation for this situation. Use the equation to find the balance in June.

Answer 1

To model this situation, we can write an equation that represents the balance in your bank account in terms of \( m \), the month number.

• In February (month 2), the balance is $270.
• Each month, you add $45 to the balance.

The equation for the balance \( B \) in month \( m \) can be written as:

\[ B(m) = 270 + 45(m - 2) \]

Here, \( (m - 2) \) represents the number of months after February.

Now, we want to find the balance in June, which is month 6:

\[ B(6) = 270 + 45(6 - 2) \] \[ B(6) = 270 + 45(4) \] \[ B(6) = 270 + 180 \] \[ B(6) = 450 \]

So, the balance in June will be $450.