The percentage, if the new cost was 84% of the original is 40%
Let the cost of the item be x.
When the price increased by y%, the new price is:
When the price decreased by the same percentage (i.e. y%), the new price is:
The cost is said to be 84% of the original price.
So, we have:
Divide both sides by x
Apply the difference of two squares
Subtract 1 from both sides of the equation
Cancel out the common factors
Take the square root of both sides
Multiply both sides by 100
Hence, the percentage is 40%
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