This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
$51
11) In a sale, the prices of coats are reduced by 15%.
*a) The original price of a coat is 15%100% - 15% = 85% of the original price. Step 2: Calculate the sale price. $$\text{Sale Price} = 85\% \times \text{Original Price}$$ $$\text{Sale Price} = 0.85 \times \60\text{Sale Price} = $51$$ The sale price of the coat is \boxed{\51}$.
*b) The sale price of a different coat is 85%P. $$0.85 \times P = \58.14Step 2: Solve for the original price $P$.P = \frac{$58.14}{0.85}P = $68.40$$ The original price of this coat is \boxed{\68.40}$.
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11) In a sale, the prices of coats are reduced by 15%. a) The original price of a coat is 60.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.