Those sales make me wonder

Algebra Level 2

The price of an item has been lowered two times, each time by p p %.

Find p p , if the final price of the item is 19 19 % lower than the starting price.


The answer is 10.

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1 solution

Zyberg Nee
Apr 2, 2016

Let's say that the price of an item is x x . Then, we can make an equation:

x ( 1 p 100 ) 2 = x ( 1 19 100 ) x(1 - \frac{p}{100})^2 = x(1 - \frac{19}{100}) , x x cancel out and we are left with:

( 1 p 100 ) 2 = 0.81 (1 - \frac{p}{100})^2 = 0.81 , we take square root from both sides:

1 p 100 = 0.9 1 - \frac{p}{100} = 0.9

p 100 = 0.1 - \frac{p}{100} = - 0.1

p = 10 p = \boxed{10}

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