Magan went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium. Magan purchased a total of 11 cans of soup and frozen dinners which collectively contain 4750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

This problem can be modeled using a system of equations based on the given information:

### Step 1: Define the variables
Let:
- \( x \) represent the number of cans of soup.
- \( y \) represent the number of frozen dinners.

### Step 2: Create the system of equations
From the problem, we are given two key pieces of information:

1. Magan purchased a total of 11 items (cans of soup and frozen dinners). This gives us the equation:
   \[
   x + y = 11
   \]

2. The total sodium content from the cans of soup and frozen dinners is 4750 mg. Since each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium, this gives us the second equation:
   \[
   350x + 650y = 4750
   \]

### Step 3: Solve the system of equations
We will first solve the system using substitution or elimination. Let’s use substitution here:

From the first equation, solve for \( y \):
\[
y = 11 - x
\]

Substitute this into the second equation:
\[
350x + 650(11 - x) = 4750
\]

### Step 4: Simplify and solve for \( x \)
Distribute the 650:
\[
350x + 650 \cdot 11 - 650x = 4750
\]
\[
350x + 7150 - 650x = 4750
\]
Combine like terms:
\[
-300x + 7150 = 4750
\]
Subtract 7150 from both sides:
\[
-300x = 4750 - 7150
\]
\[
-300x = -2400
\]
Solve for \( x \):
\[
x = \frac{-2400}{-300} = 8
\]

### Step 5: Solve for \( y \)
Now that we know \( x = 8 \), substitute this back into the equation \( y = 11 - x \):
\[
y = 11 - 8 = 3
\]

### Conclusion:
Magan purchased **8 cans of soup** and **3 frozen dinners**.

Would you like further details or clarification on this solution?

Here are 5 related questions to expand the discussion:
1. How would the result change if each frozen dinner contained 750 mg of sodium?
2. How can you check the solution for this problem?
3. What if Magan purchased a total of 15 items instead? How would you solve it?
4. How does the elimination method compare to substitution in this problem?
5. How can you use a graphical approach to solve this system of equations?

**Tip:** Always double-check your results by substituting the values back into the original equations.

Learn how to solve a system of equations involving the purchase of soup cans and frozen dinners with given sodium content. The problem involves two linear equations and is suitable for students in Grades 8-10. Step-by-step explanation provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation