A group of 6 students went bowling. Each student rented bowling shoes for $x and spent $8 on snacks. A group of 4 adults also went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $9.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes? give an equation and steps to solve it 



Let’s break down the problem and build an equation step-by-step.

### Given Information:
1. Each student rents bowling shoes for $ x $ dollars.
2. Each student spends $8 on snacks.
3. There are 6 students.
4. Each adult rents bowling shoes for $ 2x $ dollars (twice as much as a student).
5. Each adult spends $9.50 on snacks.
6. There are 4 adults.
7. Both groups spent the same total amount.

### Step 1: Express the total cost for the group of students.
- Total cost for **one** student = cost of shoes + cost of snacks = $ x + 8 $
- For 6 students, the total cost is:
\[
6(x + 8)
\]
This simplifies to:
\[
6x + 48
\]

### Step 2: Express the total cost for the group of adults.
- Total cost for **one** adult = cost of shoes + cost of snacks = $ 2x + 9.50 $
- For 4 adults, the total cost is:
\[
4(2x + 9.50)
\]
This simplifies to:
\[
8x + 38
\]

### Step 3: Set up the equation.
Since both groups spent the same total amount, we can set their total costs equal:
\[
6x + 48 = 8x + 38
\]

### Step 4: Solve the equation.
1. Subtract $ 6x $ from both sides:
   \[
   48 = 2x + 38
   \]
2. Subtract 38 from both sides:
   \[
   10 = 2x
   \]
3. Divide both sides by 2:
   \[
   x = 5
   \]

### Step 5: Find the cost of renting shoes for an adult.
Since adults pay twice as much as students for shoes, the cost for an adult is:
\[
2x = 2(5) = 10
\]

### Final Answer:
The cost for each adult to rent bowling shoes is **$10**.

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Do you want more details, or do you have any questions about the solution? Here are 5 related questions for practice:

1. If the students had spent $10 on snacks instead, how would the cost of adult shoe rentals change?
2. What if 5 students and 3 adults went bowling under the same conditions? How would the equation change?
3. What is the total amount spent by both groups together?
4. If the adults had spent $12 on snacks, what would the cost of renting their shoes be?
5. What would happen if both students and adults spent the same amount on snacks?

**Tip:** When solving equations with variables on both sides, always aim to simplify and isolate the variable step by step.

A group of 6 students went bowling. Each student rented bowling shoes for $x and spent $8 on snacks. A group of 4 adults also went bowling and paid twice as much to rent bowling shoes as each student. Each adult also spent $9.50 on snacks. If both groups spent the same total amount, what was the cost for each adult to rent bowling shoes?

Solve a real-world algebra problem involving students and adults renting bowling shoes and purchasing snacks. Learn how to set up and solve linear equations to determine the cost of renting shoes for adults. Suitable for Grades 6-8 students.

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