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Let's break down the problem to identify the correct system of equations.

### Given Information:
- Monique buys **12 bags** of peas and corn combined: total bags = $ p + c = 12 $, where $ p $ represents the number of pea bags and $ c $ represents the number of corn bags.
- Each bag of **peas** costs **$2.89**.
- Each bag of **corn** costs **$3.25**.
- The total cost of all bags is **$37.90**.

### Step-by-step breakdown:

1. **First equation**: The total number of bags is 12, so:
   \[
   p + c = 12
   \]

2. **Second equation**: The total cost of the bags is $37.90. Since each pea bag costs $2.89 and each corn bag costs $3.25, we can write the second equation as:
   \[
   2.89p + 3.25c = 37.90
   \]

### Correct system of equations:
\[
\begin{aligned}
    p + c &= 12 \\
    2.89p + 3.25c &= 37.90
\end{aligned}
\]

Now, let's check which option matches this system of equations:

- The correct answer is: **Option 4** $ p + c = 12 $ and $ 2.89p + 3.25c = 37.90 $.

Would you like a further explanation or to explore a similar problem? Here are 5 related questions:

1. How would you solve this system of equations using substitution?
2. Can you solve the system using the elimination method?
3. What if the total price was different, say $40? How would that change the system?
4. How many bags of peas and corn would Monique have bought if all the prices were increased by 10%?
5. Can we graph these two equations to find the solution visually?

**Tip:** When dealing with word problems, it's important to translate the words into algebraic expressions step by step to avoid errors.

Monique likes to make vegetable soup that uses frozen peas and sweet corn. She sees them on sale, and grabs 12 bags total of peas and corn. Each bag of peas cost $2.89 and each bag of corn cost $3.25. Using the information above, build the equations for the system using 'p' for the number of bags of peas, and 'c' for the number of bags of corn. Which system of equations would be used to find out how many bags of each she purchased, if the total came to $37.90?

Discover how to solve a system of linear equations involving the purchase of peas and corn, with prices per bag and a total cost. Learn to use algebraic methods to find the quantity of each item purchased. Suitable for high school students studying algebra.

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