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.

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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.
After bowling 12 games, the total costs at Mar Vista Bowl and Pinz are the same.

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