The total cost of a pair of shoes and a tie was $52.74$52.74. If the price of the pair of shoes was $5.58$5.58 less than the tie, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places
Question
The total cost of a pair of shoes and a tie was 52.74. If the price of the pair of shoes was 5.58 less than the tie, what was the price of the pair of shoes? Express your answer as a simplified fraction or a decimal rounded to two places
Solution
Let's denote the price of the tie as T and the price of the shoes as S.
From the problem, we know two things:
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The total cost of the tie and shoes is $52.74, so we can write this as an equation: T + S = 52.74
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The price of the shoes is $5.58 less than the tie, so we can write this as another equation: S = T - 5.58
Now we can solve this system of equations.
Substitute the second equation into the first to get: T + (T - 5.58) = 52.74
Combine like terms to get: 2T - 5.58 = 52.74
Add 5.58 to both sides to get: 2T = 58.32
Divide both sides by 2 to solve for T: T = 29.16
Now that we know the price of the tie, we can substitute it back into the second equation to find the price of the shoes: S = 29.16 - 5.58 = 23.58
So, the price of the shoes is $23.58.
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