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The total cost of a shirt and a pair of pants was [tex]$82.06. If the price of the shirt was $[/tex]0.16 less than the price of the pair of pants, what was the price of the shirt?

Express your answer as a simplified fraction or a decimal rounded to two places.

Answer: ____


Sagot :

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.