Tashaun took clothes to the dry cleaners twice over the past month. He took 4 pairs of pants and 2 sports coats for a total of $70.94 before taxes. The second time he took 3 pairs of pants and 3 sports coats for a total of $79.44. Set up a system of equations that models the problem. Identify all variables.

To set up a system of equations that models this problem, we need to define variables for the cost of cleaning pants and sports coats. Let:

- $ x $ represent the cost of cleaning one pair of pants.
- $ y $ represent the cost of cleaning one sports coat.

### First Cleaning Trip:
- Tashaun took 4 pairs of pants and 2 sports coats, and the total cost was $70.94.
- This can be modeled as the equation:  
  \[
  4x + 2y = 70.94
  \]

### Second Cleaning Trip:
- Tashaun took 3 pairs of pants and 3 sports coats, and the total cost was $79.44.
- This can be modeled as the equation:  
  \[
  3x + 3y = 79.44
  \]

### System of Equations:
Thus, the system of equations that models the problem is:
\[
\begin{aligned}
  4x + 2y &= 70.94 \\
  3x + 3y &= 79.44
\end{aligned}
\]

Here, $ x $ is the cost of cleaning one pair of pants, and $ y $ is the cost of cleaning one sports coat.

Would you like to solve this system of equations? If not, feel free to ask any other questions.

### Follow-up Questions:
1. How would you solve this system of equations using substitution?
2. Can you solve this system using the elimination method?
3. What happens to the total cost if Tashaun brings 5 pairs of pants and 4 sports coats?
4. What is the average cost per item on each trip?
5. How would the system of equations change if taxes were included?

**Tip**: When setting up systems of equations, always ensure that each equation represents a distinct event or scenario.

Learn how to set up a system of equations for Tashaun's dry cleaning costs. This problem involves creating equations to model real-world scenarios using algebra and systems of linear equations. Suitable for Grades 8-10, this example explores variables for pants and sports coats and demonstrates solution methods like substitution and elimination.

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