A group of 7 students went bowling. Each student rented bowling shoes for $x and spent $15 on snacks. A group of 6 adults also went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $12.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes?

We are asked to find the cost for each adult to rent bowling shoes given that a group of 7 students and a group of 6 adults spent the same total amount at a bowling event.

Let’s define:
- $ x $ as the cost for each student to rent bowling shoes.
- The cost for each adult to rent bowling shoes is $ 2x $ since it’s given that adults paid twice as much as students.

### Step 1: Total cost for students
Each student spent:
- $ x $ dollars on shoes.
- 15 dollars on snacks.

Thus, the total cost for one student is $ x + 15 $. Since there are 7 students, the total cost for the group of students is:
\[
7(x + 15) = 7x + 105
\]

### Step 2: Total cost for adults
Each adult spent:
- $ 2x $ dollars on shoes.
- 12.50 dollars on snacks.

Thus, the total cost for one adult is $ 2x + 12.50 $. Since there are 6 adults, the total cost for the group of adults is:
\[
6(2x + 12.50) = 12x + 75
\]

### Step 3: Set the total costs equal
Since both groups spent the same total amount, we can set the total costs equal to each other:
\[
7x + 105 = 12x + 75
\]

### Step 4: Solve for $ x $
First, subtract $ 7x $ from both sides:
\[
105 = 5x + 75
\]

Now, subtract 75 from both sides:
\[
30 = 5x
\]

Finally, divide by 5:
\[
x = 6
\]

### Step 5: Find the cost for each adult
Since each adult pays $ 2x $ for shoes, the cost for each adult to rent bowling shoes is:
\[
2x = 2(6) = 12
\]

Thus, the cost for each adult to rent bowling shoes is **$12**.

Would you like further details or have any other questions?

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Here are 5 related questions to explore:
1. How would the solution change if the adult's shoe rental was 3 times that of the students?
2. What would be the total cost for the group of adults if each student paid $8 for shoes?
3. What is the combined total spent by both groups?
4. How much would each student pay if the group of students spent $30 less than the group of adults?
5. What if an additional student joined the group, how would that affect the total amount spent by both groups?

**Tip**: When solving word problems, always define variables clearly and break down the problem step by step to avoid confusion.

Discover how to calculate the cost for each adult to rent bowling shoes using algebra. This problem compares the total expenses of two groups—students and adults—where students rent shoes for $x and adults pay twice as much. Suitable for Grades 6-8.

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