#### Posers and Puzzles

60.13N / 25.01E

- Joined
- 19 Sep '11
- Moves
- 45046

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?

127.0.0.1

- Joined
- 18 Dec '03
- Moves
- 16018

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

Reveal Hidden Contentp = -1/2 + sqrt(5)/2 ~= 0.618

60.13N / 25.01E

- Joined
- 19 Sep '11
- Moves
- 45046

Reveal Hidden ContentIndeed it is. The golden ratio once again.