Midori's favorite food is pasta. At the grocery store, he bought 1 package of cheese, 2 boxes of pasta, and 3 jars of marinara sauce for $16.22. The next week he bought 2 packages of cheese, 1 box of pasta, and 1 jar of marinara sauce for $12.99. The third week he bought 1 package of cheese, 1 box of pasta, and 1 jar of marinara sauce for $8.74.Choose the system of equations that can be solved to find the costs of cheese, c, pasta, p, and sauce, s.A.c+2c+c=16.222p+p+p=12.993s+s+s=8.74B.c+2c+c=37.952p+p+p=37.953s+s+s=37.95C.c+2p+3s=37.952c+p+s=37.95c+p+s=37.95D.c+2p+3s=16.222c+p+s=12.99 c+p+s=8.74

To find the costs of cheese (c), pasta (p), and sauce (s), we need to set up a system of equations that represents the information given in the problem.

### Information provided:
1. **First week**: 1 package of cheese, 2 boxes of pasta, and 3 jars of marinara sauce for $16.22.
2. **Second week**: 2 packages of cheese, 1 box of pasta, and 1 jar of marinara sauce for $12.99.
3. **Third week**: 1 package of cheese, 1 box of pasta, and 1 jar of marinara sauce for $8.74.

From this, we can form the following system of equations:

\[
\begin{aligned}
1. & \quad c + 2p + 3s = 16.22 \\
2. & \quad 2c + p + s = 12.99 \\
3. & \quad c + p + s = 8.74
\end{aligned}
\]

This system of equations can be solved to find the values of $ c $, $ p $, and $ s $.

### Correct option: **D** 
\[
c + 2p + 3s = 16.22, \quad 2c + p + s = 12.99, \quad c + p + s = 8.74
\]

Would you like me to solve this system of equations to find the costs of cheese, pasta, and sauce? 

### Related Questions:
1. How do you solve systems of equations using substitution?
2. What is the elimination method in solving systems of equations?
3. How can you represent this situation graphically?
4. How do the coefficients in each equation relate to the quantities of each item purchased?
5. How can matrices be used to solve a system of equations?

### Tip: 
When setting up a system of equations, make sure each equation corresponds exactly to one scenario with consistent variables for each unknown.

Midori's favorite food is pasta. At the grocery store, he bought 1 package of cheese, 2 boxes of pasta, and 3 jars of marinara sauce for $16.22. The next week he bought 2 packages of cheese, 1 box of pasta, and 1 jar of marinara sauce for $12.99. The third week he bought 1 package of cheese, 1 box of pasta, and 1 jar of marinara sauce for $8.74. Choose the system of equations that can be solved to find the costs of cheese, c, pasta, p, and sauce, s.

Learn how to solve a system of equations involving the prices of cheese, pasta, and marinara sauce using algebra. This problem features three different purchase scenarios, with equations to determine the cost of each item. Suitable for students in Grades 8-10.

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