Question

Leah starts with $250 in her bank account. Every week she withdraws $20 for miscellaneous expenses. For how many weeks could she withdraw the money if she maintains a balance of at least $90?
Write an inequality to represent the situation. Use x to represent the number of weeks.

Answer 1

To represent the situation with an inequality, we can start by determining how much Leah withdraws over time. She starts with $250 and withdraws $20 for each week. After \( x \) weeks, the amount she has withdrawn is \( 20x \).

Since Leah wants to maintain a balance of at least $90, we can express this with the inequality:

\[
250 - 20x \geq 90
\]

Now, we can solve for \( x \):

1. Subtract 250 from both sides:

\[
-20x \geq 90 - 250
\]

\[
-20x \geq -160
\]

2. Divide both sides by -20 (remember to flip the inequality sign):

\[
x \leq \frac{-160}{-20}
\]

\[
x \leq 8
\]

So, Leah can withdraw money for a maximum of \( x \leq 8 \) weeks while maintaining a balance of at least $90.

In conclusion, the inequality that represents the situation is:

\[
250 - 20x \geq 90
\]

And Leah can withdraw money for a maximum of 8 weeks.