A laser tag arean sells two types of memberships. One package costs `$325` for one year of membership with an unilimated number of visits. The second package has a `$125` enrollment fee, includes five free visits, and costs and additional `$8` per visit after the first five. How many visits over a one-year period would a person who purchese the second package need to use for teh cost to equal that of the one-year membership ?

Options

A. 20
B. 25
C. 30
D. 40

Explanation

To find out how many visits a person would need to make using the second package for the cost to equal that of the one-year membership, we can set up an equation based on the costs of both packages.

### Step-by-Step Solution:

1. **Identify the Costs**:
- The cost of the first package (unlimited visits) is **$325**.
- The second package has a **$125** enrollment fee, includes **5 free visits**, and costs **$8** for each visit after the first five.

2. **Set Up the Equation**:
- Let \( V \) be the total number of visits made in a year using the second package.
- The cost of the second package can be expressed as:
\[ \text{Cost of second package} = 125 + 8(V - 5) \]
- Here, \( V - 5 \) represents the visits beyond the initial 5 free visits.

3. **Equate the Costs**:
- We want the cost of the second package to equal the cost of the first package:
\[ 325 = 125 + 8(V - 5) \]

4. **Simplify the Equation**:
- Distributing the \( 8 \) in the equation:
\[ 325 = 125 + 8V - 40 \]
- Combine like terms:
\[ 325 = 85 + 8V \]

5. **Isolate \( V \)**:
- Subtract \( 85 \) from both sides:
\[ 325 - 85 = 8V \]
\[ 240 = 8V \]
- Divide both sides by \( 8 \):
\[ V = \frac{240}{8} \]
\[ V = 30 \]

6. **Conclusion**:
- A person would need to make **30 visits** in a year using the second package for the cost to equal that of the one-year membership.