A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 8 granola bars and each large box has 12 granola bars. The camp bought 3 times as many small boxes as large boxes, which altogether had 72 granola bars. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.

Let's define the variables first:

- Let \( x \) represent the number of small boxes purchased.
- Let \( y \) represent the number of large boxes purchased.

Now, we can write the system of equations based on the problem:

1. **Equation for the relationship between small and large boxes:**

   The camp bought 3 times as many small boxes as large boxes, so:
   \[
   x = 3y
   \]

2. **Equation for the total number of granola bars:**

   Each small box has 8 granola bars, and each large box has 12 granola bars. Altogether, there are 72 granola bars:
   \[
   8x + 12y = 72
   \]

So, the system of equations is:
\[
\begin{aligned}
x & = 3y \\
8x + 12y & = 72
\end{aligned}
\]

### Summary:
- \( x \): number of small boxes.
- \( y \): number of large boxes.
- The system of equations:
  \[
  \begin{aligned}
  x & = 3y \\
  8x + 12y & = 72
  \end{aligned}
  \]

Would you like to see the solution for this system, or do you have any other questions?

Here are 5 related questions you might consider:
1. How many small boxes were purchased if the system is solved?
2. How many large boxes were purchased?
3. What would the system of equations look like if each small box had 10 granola bars instead of 8?
4. How would the total number of granola bars change if they purchased one more large box?
5. What if the camp had bought 5 times as many small boxes as large boxes?

**Tip:** When creating a system of equations, always double-check that each equation correctly represents the relationships described in the problem.

Discover how to solve a system of linear equations to determine the number of small and large granola boxes purchased by a summer camp. This problem involves key algebraic concepts like linear equations and system of equations, perfect for Grades 6-8 students.

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