Let's solve this problem step by step.
1. Assign Variables:
Let's denote the price of the pair of pants as [tex]\( p \)[/tex].
Given that the price of the shirt is [tex]$0.16 less than the pair of pants, the price of the shirt will be \( p - 0.16 \).
2. Set Up the Equation:
According to the problem, the total cost of the shirt and the pair of pants is $[/tex]82.06. Therefore, we can write the equation:
[tex]\[
p + (p - 0.16) = 82.06
\][/tex]
3. Simplify the Equation:
Combine the terms involving [tex]\( p \)[/tex]:
[tex]\[
2p - 0.16 = 82.06
\][/tex]
4. Solve for [tex]\( p \)[/tex]:
Add 0.16 to both sides of the equation to isolate the term with [tex]\( p \)[/tex]:
[tex]\[
2p = 82.06 + 0.16
\][/tex]
[tex]\[
2p = 82.22
\][/tex]
Now, divide both sides by 2 to solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{82.22}{2}
\][/tex]
[tex]\[
p = 41.11
\][/tex]
5. Find the Price of the Shirt:
Now we know the price of the pants ([tex]\( p = 41.11 \)[/tex]). Substitute [tex]\( p \)[/tex] back into the expression for the price of the shirt:
[tex]\[
\text{Price of the shirt} = p - 0.16
\][/tex]
[tex]\[
\text{Price of the shirt} = 41.11 - 0.16
\][/tex]
[tex]\[
\text{Price of the shirt} = 40.95
\][/tex]
Therefore, the price of the shirt is $40.95.
