SOLUTION: The price of an item that sold for $240 was reduced by 33 1/3%. By what percent must the price of the item be increased to bring the price back to $240?

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: The price of an item that sold for $240 was reduced by 33 1/3%. By what percent must the price of the item be increased to bring the price back to $240?      Log On


   

Question 1026453: The price of an item that sold for $240 was reduced by 33 1/3%. By what percent must the price of the item be increased to bring the price back to $240?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The price really doesn't matter, so
I'll just say it is +p+
I'll convert the % to equivilant fraction
It was sold for +p+-+%281%2F3%29%2Ap+=+%282%2F3%29%2Ap+
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Let +k+ = the fraction to factor by
Now you want:
+k%2A%28+2%2F3+%29%2Ap+=+p+
Divide both sides by +p+
+k%2A%28+2%2F3+%29+=+1+
+k+=+%28+3%2F2+%29+
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So I have:
+%283%2F2%29%2A%282%2F3%29%2Ap+=+p+
+%28+1+%2B+1%2F2+%29%2A%28+2%2F3%29%2Ap+=+p+
+%28+2%2F3%29%2Ap+%2B+%281%2F2%29%2A%28+2%2F3%29%2Ap+=+p+
So, +%282%2F3%29%2Ap+ must be increased by +1%2F2+ or 50%
to get back to +p+ ( which is $240 in this case )