To determine after how many months Alma will have [tex]$145 left in her bank account, follow these steps:
1. Identify the given equation and the value of \( y \) we need to find:
The equation given is:
\[
y = -27x + 577
\]
where \( y \) represents the amount of money left in Alma's account, and \( x \) represents the number of months. We need to find \( x \) when \( y = 145 \).
2. Set up the equation with the given \( y \) value:
Substitute \( y = 145 \) into the equation:
\[
145 = -27x + 577
\]
3. Solve for \( x \):
- First, isolate the term with \( x \) on one side of the equation. Subtract 577 from both sides:
\[
145 - 577 = -27x
\]
Simplify the left-hand side:
\[
-432 = -27x
\]
- Next, solve for \( x \) by dividing both sides of the equation by -27:
\[
x = \frac{-432}{-27}
\]
Simplify the fraction:
\[
x = 16
\]
4. Conclusion:
Alma will have $[/tex]145 left in her account after 16 months.
Thus, the correct answer is:
[tex]\[
\boxed{16 \text{ months}}
\][/tex]
