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.
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 250 - 20x = 90, to find the boundary for the inequality. Show your work or solve on paper.
250 - 20x ≥ 90
250−20x
=
90

x
=

Answer 1

To represent Leah's situation with an inequality, we start with her initial bank balance and account for her weekly withdrawals. Leah starts with $250 and withdraws $20 each week. She wants to maintain a balance of at least $90.

The inequality can be set up as follows:

\[
250 - 20x \geq 90
\]

Now, let's solve the associated equation \(250 - 20x = 90\) to find the boundary for the inequality.

1. Start with the equation:
\[
250 - 20x = 90
\]

2. Subtract 250 from both sides:
\[
-20x = 90 - 250
\]
\[
-20x = -160
\]

3. Divide both sides by -20. Remember, when we divide or multiply an inequality by a negative number, we flip the inequality sign, but since we are working with an equation here, we do not need to flip the sign:
\[
x = \frac{-160}{-20}
\]
\[
x = 8
\]

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

Now let's review our inequality once more:
\[
250 - 20x \geq 90
\]
This inequality shows the condition that the amount left in Leah's bank account after \(x\) weeks must be greater than or equal to $90.

Thus, the final result:
\[
x \leq 8
\]
indicating that Leah can withdraw money for up to 8 weeks.