Two successive discounts of 50% and 50% are followed by two successive increases of 20% and 20%. What single percentage change would produce the same result?
p * (1 - .5) * (1 - .5) * (1 + .2) * (1 + .2) = ?
Is it 64% decrease? Thanks
correct
To find the single percentage change that would produce the same result, we need to calculate the net percentage change after applying the successive discounts and increases.
Let's assume the original price of the item is $100.
First discount: 50% off => $100 - (50/100 * $100) = $50
Second discount: 50% off => $50 - (50/100 * $50) = $25
Now, we have a price of $25 after the two discounts.
First increase: 20% on $25 => $25 + (20/100 * $25) = $25 + $5 = $30
Second increase: 20% on $30 => $30 + (20/100 * $30) = $30 + $6 = $36
The final price after the two increases is $36.
To calculate the overall percentage change, we need to find the difference between the final price ($36) and the original price ($100), and express it as a percentage of the original price:
Percentage change = ((Final Price - Original Price) / Original Price) * 100
= (($36 - $100) / $100) * 100
= (-$64 / $100) * 100
= -64%
Therefore, a single percentage change of -64% would produce the same result as the given successive discounts and increases.