SOLUTION: The original price of an smartphone was increased by 25%. A sale brought the price of the smartphone back down to its original price. The sale reduced the new price of the smartph

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Question 1190178: The original price of an smartphone was increased by 25%. A sale brought the price of the smartphone back down to its original price. The sale reduced the new price of the smartphone by what percent?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
p, original price

%281%2B0.25%29p, the increase


p%2F%28%281%2B0.25%29p%29, the reduced price after the increase

1%2F%281%2B0.25%29

0.8------------this is 80% of the original price, so this is 20% off from original price.

Answer by ikleyn(52752) About Me  (Show Source):
You can put this solution on YOUR website!
.
The original price of an smartphone was increased by 25%.
A sale brought the price of the smartphone back down to its original price.
The sale reduced the new price of the smartphone by what percent?
~~~~~~~~~~~~~~~~~ 

Let X be the original price of the smartphone and let "p" be the percent of the further reducing the price.


After increasing the original price, new price is 1.25X.


After reducing the price by "p" percents, the final price is %281+%2B+p%2F100%29%2A1.25X.


The problem says that the final price is the same as the very original price,
so we write this equation


    %281+%2B+p%2F100%29%2A1.25X = X.


Next, we divide both sides by X


    %281+%2B+p%2F100%29%2A1.25 = 1.


It gives us


    1%2Bp%2F100 = 1%2F1.25 = 0.8

    p%2F100 = 0.8 - 1 = -0.2

       p = -20.


It means that the reduction was 20%.      ANSWER

Solved.