The total cost of a shirt and a pair of pants was $92.12$92.12. If the price of the shirt was $1.78$1.78 less than 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.
Question
The total cost of a shirt and a pair of pants was 92.12. If the price of the shirt was 1.78 less than 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.
Solution
Let's denote the price of the shirt as S and the price of the pants as P.
From the problem, we know two things:
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S + P = 92.12 (The total cost of the shirt and pants is $92.12)
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S = P - 1.78 (The price of the shirt is $1.78 less than the price of the pants)
We can substitute the second equation into the first to solve for P:
(P - 1.78) + P = 92.12 2P - 1.78 = 92.12 2P = 92.12 + 1.78 2P = 93.9 P = 93.9 / 2 P = 46.95
Substitute P = 46.95 into the second equation to find S:
S = 46.95 - 1.78 S = 45.17
So, the price of the shirt is $45.17.
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