Samuel went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 300 mg of sodium and each frozen dinner has 450 mg of sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium. Write a system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased. Define the variables that you use to write the system.

Let's define two variables to represent the number of cans of soup and the number of frozen dinners purchased:

- Let \( x \) represent the number of cans of soup.
- Let \( y \) represent the number of frozen dinners.

### Now, we can write the system of equations based on the information provided:

1. **Sodium content equation**: 
   - Each can of soup contains 300 mg of sodium, so the total sodium from the soup is \( 300x \).
   - Each frozen dinner contains 450 mg of sodium, so the total sodium from the frozen dinners is \( 450y \).
   - Together, the total sodium from both items is 6000 mg.
   
   This gives us the first equation:
   \[
   300x + 450y = 6000
   \]

2. **Relationship between soup and dinners**:
   - Samuel purchased 5 more frozen dinners than cans of soup, so we can express this relationship as:
   \[
   y = x + 5
   \]

### System of equations:
\[
\begin{aligned}
1) \ & 300x + 450y = 6000 \\
2) \ & y = x + 5
\end{aligned}
\]

This system can now be used to determine the number of cans of soup and frozen dinners Samuel purchased.

Would you like to solve this system of equations, or would you prefer a more detailed explanation of how to solve it?

Here are 5 questions to expand on this problem:
1. How can we solve this system of equations using substitution or elimination?
2. What are the real-world implications of consuming too much sodium?
3. How would the problem change if each can of soup had 400 mg of sodium instead?
4. What if Samuel purchased 5 fewer frozen dinners than cans of soup?
5. How can we check if the solution to this system is correct?

**Tip**: When solving systems of equations, always choose the method (substitution or elimination) that simplifies the process based on the equations given.

Learn how to write a system of equations to determine the number of cans of soup and frozen dinners Samuel purchased, based on the sodium content. This problem involves creating and solving two linear equations, ideal for students in Grades 8-10.

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