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 represent the situation with a system of equations, we can define the cost equations for both Bowler World and Lucky Spares using \( g \) for the number of games and \( c \) for the total cost.

### Part A

1. **Bowler World:**
- Cost of shoes: $5.00
- Cost per game: $1.10
- Total Cost equation:
\[
c = 1.10g + 5.00
\]

2. **Lucky Spares:**
- Cost of shoes: $3.00
- Cost per game: $1.50
- Total Cost equation:
\[
c = 1.50g + 3.00
\]

So, the system of equations is:
\[
\begin{align*}
c & = 1.10g + 5.00 \quad \text{(Bowler World)} \\
c & = 1.50g + 3.00 \quad \text{(Lucky Spares)}
\end{align*}
\]

### Part B

To find for how many games the cost is the same for both locations, we set the two equations equal to each other:
\[
1.10g + 5.00 = 1.50g + 3.00
\]

Now, we can solve for \( g \):
1. Subtract \( 1.10g \) from both sides:
\[
5.00 = 0.40g + 3.00
\]

2. Subtract \( 3.00 \) from both sides:
\[
2.00 = 0.40g
\]

3. Divide by \( 0.40 \):
\[
g = \frac{2.00}{0.40} = 5
\]

Now that we have \( g = 5 \), we can find the cost by substituting \( g \) back into either equation. Let's use Bowler World’s equation:
\[
c = 1.10(5) + 5.00 = 5.50 + 5.00 = 10.50
\]

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

### Summary
- **Part A:**
- System of equations:
\[
\begin{align*}
c & = 1.10g + 5.00 \\
c & = 1.50g + 3.00
\end{align*}
\]
- **Part B:**
- The cost is the same for both locations when \( g = 5 \) games, and the cost is \( c = 10.50 \).