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Let's analyze the problem and solve it step by step.

We are given:
- The first location charges a $2.00 fee plus $7.50 per game.
- The second location charges an $8.00 fee plus $6.00 per game.

We need to find out how many games they need to play for the total cost at both locations to be equal.

### Step 1: Formulating the equation
Let $ x $ represent the number of games.

For the first location:
\[
\text{Total cost} = 2 + 7.5x
\]

For the second location:
\[
\text{Total cost} = 8 + 6x
\]

We need to find the value of $ x $ for which these costs are equal:
\[
2 + 7.5x = 8 + 6x
\]

### Step 2: Solving the equation
Now, solve for $ x $:

\[
2 + 7.5x = 8 + 6x
\]

Subtract 6x from both sides:
\[
2 + 1.5x = 8
\]

Subtract 2 from both sides:
\[
1.5x = 6
\]

Divide both sides by 1.5:
\[
x = 4
\]

### Conclusion:
They would need to play **4 games** for the costs to be equal.

Would you like more details or clarification on any part of the solution?

Here are five related questions to extend this topic:
1. What would the total cost be after 4 games at both locations?
2. How would the equation change if the first location's fee increased by $1?
3. If they played 6 games, which location would be cheaper, and by how much?
4. How would you set up a similar problem for different types of fees, like parking charges?
5. How does the slope of the cost equation relate to the per-game price?

**Tip**: Setting up an equation and isolating the variable is a common method for solving "same cost" problems in algebra.

Ben and his friends are going to play putt putt. One location charges a $2.00 fee plus $7.50 per game. A second location charges an $8.00 fee plus $6.00 per game. How many games would they have to play for both locations to cost the same amount?

Learn how to solve a cost comparison problem involving linear equations for two putt putt locations. We calculate the number of games needed for the total cost at both locations to be equal. This problem covers key algebra concepts suitable for Grades 6-8.

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