https://file.aiquickdraw.com/mathbot/file/1729472267404xmiazh57.jpg

Let's analyze the problem and the system of equations.

### Problem Breakdown:
- Monique is purchasing frozen peas and corn.
- She buys **12 bags in total** of peas and corn combined.
- The **cost per bag** of peas is **$2.89**, and the **cost per bag** of corn is **$3.25**.
- The **total cost** for all bags is **$37.90**.

### Variables:
- Let **p** represent the number of bags of peas.
- Let **c** represent the number of bags of corn.

### First Equation:
The total number of bags purchased is 12, so:
\[
p + c = 12
\]

### Second Equation:
The total cost is $37.90. The cost of peas is $2.89 per bag, and the cost of corn is $3.25 per bag. Therefore, the total cost equation is:
\[
2.89p + 3.25c = 37.90
\]

### System of Equations:
\[
\begin{cases}
p + c = 12 \\
2.89p + 3.25c = 37.90
\end{cases}
\]

Looking at the options provided in the image, the correct one is:

\[
p + c = 12 \quad \text{and} \quad 2.89p + 3.25c = 37.90
\]

This corresponds to **Option B** (the second option).

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Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you solve a system of equations like this using substitution or elimination?
2. How would the equations change if the cost of corn or peas changed?
3. What if Monique bought 15 bags instead of 12—how would the system of equations adjust?
4. How can you graphically represent this system of equations?
5. What is the relationship between the cost per bag and the total cost in this problem?

**Tip:** For solving systems of equations, using substitution or elimination can simplify your approach significantly when working with real-world problems.

Monique likes to make vegetable soup that uses frozen peas and sweet corn. She buys 12 bags total of peas and corn. Each bag of peas costs $2.89 and each bag of corn costs $3.25. Using the given information, which system of equations would be used to find out how many bags of each she purchased if the total cost is $37.90?

Learn how to solve a system of linear equations to determine how many bags of peas and corn Monique bought. This problem uses two equations based on total bags and total cost, providing a step-by-step solution.

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