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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.

y – 270 = 45x; $45

y = 45(x – 4); $270

y – 270 = 45(x – 2) ; $450

y = 45(x – 4); $180

1 answer

To create an equation to represent the situation, we start with the initial balance in February ($270) and add the monthly deposits of $45 for each month that passes.

We denote:

  • \( y \) as the balance in the bank account,
  • \( x \) as the month number (with January = 1, February = 2, and so on).

Since the deposits begin in February, we can establish that the balance grows each month based on how many months have passed since February.

The equation that accurately fits this situation is:

\[ y = 270 + 45(x - 2) \]

This accounts for the initial balance of $270 in February and adds $45 for each month after that (with February being month 2).

Now, let's find the balance in June (which is month 6, so \( x = 6 \)):

  1. Substitute \( x = 6 \) into the equation:

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

So the balance in June is $450.