SOLUTION: A store reduces the price of a CD player by 20% and then reduces that price by 15%.If the final price of the CD player is $170, what was its original price?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A store reduces the price of a CD player by 20% and then reduces that price by 15%.If the final price of the CD player is $170, what was its original price?      Log On


   

Question 1154593: A store reduces the price of a CD player by 20% and then reduces that price by 15%.If the final price of the CD player is $170, what was its original price?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
p-p%2F5, the first discount.

%28p-p%2F5%29-0.15%28p-p%2F5%29, the second discount.

NOT the only way.

%28p-p%2F5%29-0.15%28p-p%2F5%29=170-------simplify and solve.

Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the original price be x.


Then after first reduction the price is  

    x - 0.2x = x*(1-0.2) = 0.8x.



Next, after the second reduction, the price is  

    0.8x - 0.15*(0.8x)) = 0.8x*(1-0.15) = 0.8x*0.85 = 0.8*0.85x = 0.68x.



You are given that

    0.68x = 170  dollars.



Hence,  x = 170%2F0.68 = 250.



ANSWER.  The original price was 250 dollars.

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Then you have a problem like this one with the chain of discounts, it is important to understand that the final
discounted price is the product of the original price and some number of simple factors.

You must know what these factors are and how to solve such problems quickly in couple of lines (and a couple of minutes).

Learn it from my post.

In this problem,  the first factor is  1-0.2 = 0.8;   the second factor is  1-0.15 = 0.85.

So, each factor is the complement of a discount value (presented as decimal) to 1.