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.
Nice!
You just wrote an inequality to represent the situation. Now solve the associated equation, 200 - 15x = 65, to find the boundary for the inequality. Show your work or solve on paper.
200 - 15x ≥ 65
200−15x
=
65
−
−
=

x
=
Excellent!
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= 8 x=9 (boundary) x= 10
200 - 15x ≥ 65

Answer 1

Let's start by solving the inequality and the equation you've mentioned:

1. **Inequality:**
\[ 200 - 15x \geq 65 \]

2. **Associated equation:**
\[ 200 - 15x = 65 \]

Now, we'll solve the equation to find the boundary:

\[
200 - 15x = 65
\]

Subtract 200 from both sides:

\[
-15x = 65 - 200
\]
\[
-15x = -135
\]

Now, divide by -15 (remember that dividing by a negative reverses the inequality):

\[
x = \frac{-135}{-15}
\]
\[
x = 9
\]

So, the boundary is \( x = 9 \) weeks.

### Now we'll fill in the table to evaluate the inequality \( 200 - 15x \geq 65 \):

#### For \( x = 8 \):
\[
200 - 15(8) = 200 - 120 = 80
\]
\[
80 \geq 65 \quad \text{(True)}
\]

#### For \( x = 9 \) (boundary):
\[
200 - 15(9) = 200 - 135 = 65
\]
\[
65 \geq 65 \quad \text{(True)}
\]

#### For \( x = 10 \):
\[
200 - 15(10) = 200 - 150 = 50
\]
\[
50 \geq 65 \quad \text{(False)}
\]

### Summary Table

| \( x \) | Expression \( 200 - 15x \geq 65 \) | Result |
|---------|-------------------------------------|---------|
| 8 | \( 80 \geq 65 \) | True |
| 9 | \( 65 \geq 65 \) | True |
| 10 | \( 50 \geq 65 \) | False |

So, according to the situation, Michael could withdraw money for 9 weeks while maintaining at least $65 in his account.