Percentages

A post-xmas sale promised reductions of price ranging to 30 to 70 percent. Seeing that 30+70 = 100 had me thinking..

A company increases the price of a product by p%, then reduces it by q% so that p + q = 100. How much is p, if two changes cancel each other out?

Well
1 + p has an inverse relation ship with 1 - q if the two cancel each other out, and since p + q = 1, then 1 - q = p:

(1 + p) * p = 1

p^2 + p - 1 = 0

The quadratic formula makes that

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