In a certain clothing store, 6 shirts and 3 ties cost $79.50, and 3 shirts and 2 ties cost $41. Determine the cost of each shirt.

Answer: $12

Step-by-step explanation:

For this problem, we can use system of equations to solve. Let's use x for shirts and y for ties.

Equation 1

6x+3y=79.5

This equation comes from the first sentence. 79.5 is the total cost.

Equation 2

3x+2y=41

This equation comes from the second part of the first sentence. 41 is the total cost.

Since we are looking for the cost of each shirt, let's use the elimination method to eliminate y. First, we need to multiply both equations to that the y in both equations equal each other.

2 (6x+3y=79.5)

3 (3x+2y=41)

Now that we have chosen a common number, we can multiply.

12x+6y=159

9x+6y=123

We can now subtract both equations to cancel out y.

3x=36

Divide to get x alone.

x=12

Each shirt costs $12.