The cost of a gym membership is a onetime fee of $140, plus a monthly fee of $ 40. Brendan wrote a $500 check to pay his gym membership for a certain number of months, including the onetime fee. How many months of membership did he pay for?

Options

A. 3
B. 4
C. 9
D. 12

Answer

To solve the problem, we need to determine how many months of gym membership Brendan paid for with his $500 check. The total cost consists of a one-time fee and a monthly fee.

### Step-by-Step Solution:

1. **Identify the Costs**:
- One-time fee for gym membership: $140
- Monthly fee: $40

2. **Set Up the Equation**:
Let \( x \) be the number of months Brendan paid for. The total cost for \( x \) months can be expressed as:
\[ \text{Total Cost} = \text{One-time fee} + (\text{Monthly fee} \times \text{Number of months}) \]
This can be written as:
\[ 500 = 140 + 40x \]

3. **Isolate the Variable**:
To find \( x \), we first subtract the one-time fee from both sides of the equation:
\[ 500 - 140 = 40x \]
Simplifying this gives:
\[ 360 = 40x \]

4. **Solve for \( x \)**:
Now, divide both sides by 40 to solve for \( x \):
\[ x = \frac{360}{40} \]
Simplifying this gives:
\[ x = 9 \]

5. **Conclusion**:
Brendan paid for 9 months of gym membership.