SOLUTION: The price of a refrigerator decrease by 20%and then by 25%. By what percent must the price increase to reach the original price

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The price of a refrigerator decrease by 20%and then by 25%. By what percent must the price increase to reach the original price       Log On


   

Question 844163: The price of a refrigerator decrease by 20%and then by 25%. By what percent must the price increase to reach the original price
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
p = original price.

Decrease 20%.
p-p%2820%2F100%29=p%281-1%2F5%29
%288%2F10%29p

Decrease 25% from (8/10)p.
%288%2F10%29p-%2825%2F100%29%288%2F10%29p
%288%2F10%29p%281-25%2F100%29
%288%2F10%29p%283%2F4%29
%288%2F10%29%283%2F4%29p
%284%2F5%29%283%2F4%29p
highlight_green%28%283%2F5%29p%29

The 20% and then the 25% decreases were effectively a decrease of %282%2F5%29 of the original price, which is a 40% decrease from the original price p.

The question is, starting from %283%2F5%29p, what is the percent increase to reach 1%2Ap?

Let m be a factor so that %283%2F4%29p%2Am=p. What is the value of this factor, m? No steps needed hopefully, for seeing that highlight_green%28m=5%2F3%29. As the percent increase, this is m=5%2F3=1%262%2F3; the two-thirds part being the fraction of the increase needed. As a percentage, this is highlight%2866%262%2F3%29 percent increase.