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?

Question

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.