Signs in a department store read, "75% off original prices when you take an extra extra 50% off already reduced prices." By what percent were original prices reduced before today's sale?
To calculate the percentage by which the original prices were reduced before today's sale, we can work through the problem step by step.
Let's assume the original price of an item was $100.
First, we calculate the reduced price after the initial discount of 75% off the original price:
Reduced price = Original price - (75% of Original price)
Reduced price = $100 - (0.75 * $100) = $100 - $75 = $25.
Next, we calculate the further reduction after taking an additional 50% off the already reduced price:
Final price = Reduced price - (50% of Reduced price)
Final price = $25 - (0.5 * $25) = $25 - $12.50 = $12.50.
Now, we compare the final price to the original price to find the percentage reduction:
Percentage reduction = ((Original price - Final price) / Original price) * 100%
Percentage reduction = (($100 - $12.50) / $100) * 100% = (87.50 / $100) * 100% = 87.5%.
Therefore, the original prices were reduced by 87.5% before today's sale.