To determine the price of one shirt, we can set up and solve a system of linear equations based on the purchases described.
Step 1: Define the variables
Let's denote:
- [tex]\( s \)[/tex] as the price of one shirt
- [tex]\( p \)[/tex] as the price of one pant
Step 2: Create the equations
Based on the information given, we can write two equations:
1. For the scenario where 3 shirts and 2 pants cost [tex]$104.81:
\[
3s + 2p = 104.81
\]
2. For the scenario where 2 shirts and 1 pant cost $[/tex]61.33:
[tex]\[
2s + p = 61.33
\][/tex]
Step 3: Solve the system of equations
We will solve these two equations simultaneously to find the values of [tex]\( s \)[/tex] and [tex]\( p \)[/tex].
First, solve the second equation [tex]\( 2s + p = 61.33 \)[/tex] for [tex]\( p \)[/tex]:
[tex]\[
p = 61.33 - 2s
\][/tex]
Next, substitute [tex]\( p = 61.33 - 2s \)[/tex] into the first equation:
[tex]\[
3s + 2(61.33 - 2s) = 104.81
\][/tex]
Simplify and solve for [tex]\( s \)[/tex]:
[tex]\[
3s + 122.66 - 4s = 104.81
\][/tex]
[tex]\[
-s + 122.66 = 104.81
\][/tex]
[tex]\[
-s = 104.81 - 122.66
\][/tex]
[tex]\[
-s = -17.85
\][/tex]
[tex]\[
s = 17.85
\][/tex]
Therefore, the price of one shirt is:
[tex]\[
\boxed{17.85}
\][/tex]
