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A store has a 25% off sale on coats. With this discount, the price of one coat is $34.50. What is the original price of the coat? $

A store has a 25% 25 \% off sale on coats. With this discount, the price of one coat is $34.50 \$ 34.50 .\newlineWhat is the original price of the coat?\newline$ \$

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Full solution

Q. A store has a 25% 25 \% off sale on coats. With this discount, the price of one coat is $34.50 \$ 34.50 .\newlineWhat is the original price of the coat?\newline$ \$
  1. Calculate Discounted Price: To find the original price of the coat, we need to determine what $34.50\$34.50 represents after a 2525% discount. Since the discount is 2525%, the $34.50\$34.50 is actually 7575% of the original price, because 100%−25%=75%100\% - 25\% = 75\%. We can set up the equation where 7575% of the original price (OP) equals $34.50\$34.50. Mathematically, this is represented as 0.75×OP=$34.500.75 \times OP = \$34.50.
  2. Find Original Price: To find the original price (OP), we need to divide the discounted price by 0.750.75. So, OP=$34.500.75\text{OP} = \frac{\$34.50}{0.75}.
  3. Perform Division: Now we perform the division to find the original price. OP=$34.50/0.75=$46.00OP = \$34.50 / 0.75 = \$46.00.

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