Q-> There is a series of two discount of x% on an item. The final price is tagged at 36% of original price. what is the value of x.
Use numbers.
Say original price = 100. That means final price = 36.
We know that the item is discounted twice by x%.
Discounting one time would yield 100*(1-x). Then you discount it again by multiplying by (1-x) to arrive at final price of 36. Therefore:
Original equation: 100*(1-x)*(1-x) = 36
group common terms: 100*(1-x)^2 = 36
Divide both sides by 100: (1-x)^2 = 36/100
Take square root of both sides: (1-x) = 6/10
Solve for x: x = 1 - 6/10 = 4/10 = 40%
Check answer:
Original price of 100 discounted one time gives you 100*(1-.4) = 60. Discount the 60 by 40% one more time to give you 60*(1-.4) = 36. Done.
