Question

Bowler World charges $5.00 to rent
shoes and $1.10 per game. Lucky
Spares charges $3.00 for shoes and
$1.50 per game.
Part A
Write a system of equations to
represent the situation, using g for
number of games and c for cost.
Part B
For how many games is the cost the
same for both locations? What is
that cost?

Answer 1

To solve the problem, let's establish the costs at each location based on the given rates.

### Part A

1. **Bowler World**:
- Cost of shoes: $5.00
- Cost per game: $1.10
- Total cost (c) for Bowler World can be represented as:
\[
c = 5 + 1.10g
\]

2. **Lucky Spares**:
- Cost of shoes: $3.00
- Cost per game: $1.50
- Total cost (c) for Lucky Spares can be represented as:
\[
c = 3 + 1.50g
\]

Now we can write the system of equations:

\[
\begin{align*}
1. & \quad c = 5 + 1.10g \quad \text{(Bowler World)} \\
2. & \quad c = 3 + 1.50g \quad \text{(Lucky Spares)}
\end{align*}
\]

### Part B

To find out for how many games the cost is the same at both locations, we need to set the two equations equal to each other and solve for \(g\):

\[
5 + 1.10g = 3 + 1.50g
\]

Now, let's isolate \(g\):

1. Subtract \(1.10g\) from both sides:
\[
5 = 3 + 0.40g
\]

2. Subtract 3 from both sides:
\[
2 = 0.40g
\]

3. Divide both sides by 0.40:
\[
g = \frac{2}{0.40} = 5
\]

Now that we have \(g = 5\), we can find the cost at either location:

Using Bowler World’s equation:
\[
c = 5 + 1.10(5) = 5 + 5.50 = 10.50
\]

Thus, the cost is the same for both locations when \(g = 5\) games, and that cost is **$10.50**.

### Summary
- **Number of games** for equal cost: \( 5 \)
- **Cost at that point**: \( \$10.50 \)