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? write an equation

Let's break the problem down step by step and set up an equation.

### Given:
- There are **6 students**. 
  - Each student rents bowling shoes for **$x**.
  - Each student spends **$8** on snacks.
- There are **4 adults**.
  - Each adult rents bowling shoes for **2x** (twice as much as a student).
  - Each adult spends **$9.50** on snacks.
  
The total cost for both groups is equal.

### Cost for students:
For 6 students:
- **Shoe rental cost**: $ 6 \times x $
- **Snacks cost**: $ 6 \times 8 = 48 $

Total cost for the students is:
\[
6x + 48
\]

### Cost for adults:
For 4 adults:
- **Shoe rental cost**: $ 4 \times 2x = 8x $
- **Snacks cost**: $ 4 \times 9.50 = 38 $

Total cost for the adults is:
\[
8x + 38
\]

### Equation:
Since both groups spent the same total amount, set the two expressions equal to each other:
\[
6x + 48 = 8x + 38
\]

Now you can solve this equation to find the value of $x$, the cost for each student to rent bowling shoes. Then, the cost for each adult to rent shoes will be $2x$.

Would you like me to solve this equation or provide more details on the process?

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Here are 5 related questions to expand on this topic:
1. What is the value of $x$ once you solve the equation?
2. How much did the entire group of 6 students spend?
3. How much did the entire group of 4 adults spend?
4. If an additional fee was added for lane rental, how would that affect the equation?
5. What would happen if the price of snacks for the adults increased by 20%?

**Tip:** Always double-check the coefficients in an equation before solving, as small errors can lead to incorrect results!

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?

Learn how to solve a linear equation involving a group of students and adults renting bowling shoes and buying snacks. This problem involves calculating the cost of rentals and snacks and setting up an equation to find the price of shoe rentals. Suitable for students in Grades 6-8.

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