You bowl at Mar Vista Bowl, where renting shoes costs \( \$ 2 \) and each game bowled is \( \$ 3.50 \). Your friend bowls at Pinz where the shoe rental is \( \$ 5 \) and each game bowled is \( \$ 3.25 \). Write and solve an equation to find the number of games for which the total cost will be the same for the two bowling alleys.

To determine the number of games for which the total cost at **Mar Vista Bowl** and **Pinz** will be the same, let's set up and solve an equation based on the provided costs. ### **Step 1: Define the Variables** Let \( x \) represent the number of games bowled. ### **Step 2: Write the Cost Equations** 1. **Mar Vista Bowl:** - **Shoe Rental:** \$2 - **Cost per Game:** \$3.50 - **Total Cost (MV):** \[ MV = 2 + 3.50x \] 2. **Pinz:** - **Shoe Rental:** \$5 - **Cost per Game:** \$3.25 - **Total Cost (P):** \[ P = 5 + 3.25x \] ### **Step 3: Set the Total Costs Equal to Each Other** To find the number of games where both bowling alleys cost the same: \[ 2 + 3.50x = 5 + 3.25x \] ### **Step 4: Solve for \( x \)** 1. **Subtract \$2 from both sides:** \[ 3.50x = 3 + 3.25x \] 2. **Subtract \( 3.25x \) from both sides:** \[ 3.50x - 3.25x = 3 \] \[ 0.25x = 3 \] 3. **Divide both sides by 0.25:** \[ x = \frac{3}{0.25} = 12 \] ### **Conclusion** The total cost at **Mar Vista Bowl** and **Pinz** will be the same after bowling **12 games**. **Verification:** - **Mar Vista Bowl:** \[ MV = 2 + 3.50 \times 12 = 2 + 42 = \$44 \] - **Pinz:** \[ P = 5 + 3.25 \times 12 = 5 + 39 = \$44 \] Both total to \$44, confirming that at **12 games**, the costs are equal. **Answer:** After bowling 12 games, the total costs at both alleys are equal.