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
=
Nice!
Fill in the table to show whether a value below the boundary, the boundary, and a value above the boundary make the inequality true or false.
x= 7 x=8 (boundary) x= 9
250 - 20x ≥ 90

Answer 1

We start with the inequality to represent Leah's situation:

\[
250 - 20x \geq 90
\]

Next, we will solve the associated equation to find the boundary for the inequality.

### Step 1: Solve the associated equation
Set the inequality to equal:

\[
250 - 20x = 90
\]

### Step 2: Isolate \( x \)

1. Subtract 250 from both sides:

\[
-20x = 90 - 250
\]

\[
-20x = -160
\]

2. Divide by -20 (remember that dividing by a negative number reverses the inequality):

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

\[
x = 8
\]

### Conclusion for the boundary
The boundary for the inequality is \( x = 8 \).

### Step 3: Fill in the table to check values

We want to check three values: below the boundary \( x = 7 \), the boundary \( x = 8 \), and above the boundary \( x = 9 \).

#### For \( x = 7 \):

\[
250 - 20(7) \geq 90
\]
\[
250 - 140 \geq 90
\]
\[
110 \geq 90 \quad \text{(True)}
\]

#### For \( x = 8 \):

\[
250 - 20(8) \geq 90
\]
\[
250 - 160 \geq 90
\]
\[
90 \geq 90 \quad \text{(True)}
\]

#### For \( x = 9 \):

\[
250 - 20(9) \geq 90
\]
\[
250 - 180 \geq 90
\]
\[
70 \geq 90 \quad \text{(False)}
\]

### Final results in the table

| \( x \) | Result |
|----------|------------------------|
| 7 | True |
| 8 (boundary) | True |
| 9 | False |

This shows that Leah can withdraw money for 8 weeks while maintaining a balance of at least $90.