Question

Michael starts with $200 in his bank account. Every week he withdraws $15 for miscellaneous expenses. For how many weeks could he withdraw the money if he maintains a balance of at least $65?
Write an inequality to represent the situation. Use x to represent the number of weeks.

Answer 1

To determine how many weeks Michael can withdraw money while maintaining a balance of at least $65, we start by defining the initial conditions and formulating the inequality.

1. **Initial Amount**: $200
2. **Withdrawal per Week**: $15
3. **Minimum Balance**: $65

After \( x \) weeks, the amount left in his bank account can be expressed as:

\[
200 - 15x
\]

We want this amount to be at least $65, which gives us the inequality:

\[
200 - 15x \geq 65
\]

To solve for \( x \), we'll subtract 200 from both sides:

\[
-15x \geq 65 - 200
\]

Calculating the right side:

\[
-15x \geq -135
\]

Next, we divide both sides by -15, remembering that dividing by a negative number reverses the inequality:

\[
x \leq \frac{-135}{-15}
\]

Calculating this gives:

\[
x \leq 9
\]

Therefore, the inequality that represents the situation is:

\[
200 - 15x \geq 65
\]

And Michael can withdraw money for a maximum of **9 weeks** while maintaining a balance of at least $65.