SOLUTION: An article is on sale for 20% off its original price. What percent of increase is needed to return the sale item to its original price? Thank you for the help.

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Question 1027624: An article is on sale for 20% off its original price. What percent of increase is needed to return the sale item to its original price?
Thank you for the help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +p+ = the original price
The sale price is:
+p+-+.2p+
+p%2A%28+1+-+.2+%29+
+.8p+
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First, I will ask: what fraction +x%2F100+
should I multiply the sale price by
and then add to +.8p+ to
get back to +p+ ?
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+%28+x%2F100+%29%2A%28+.8p+%29+%2B+.8p+=+p+
I can divide both sides by +p+
+.8%2A%28+x%2F100+%29+%2B+.8+=+1+
Divide both sides by +.8+
+x%2F100+%2B+1+=+1.25+
+x%2F100+=+.25+
+x+=+25+
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A 25% increase after the sale price is needed
to return to the original price
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check answer:
Suppose original price was $1200
+.8%2A1200+=+960+
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Now a 25% increase means factoring by +1.25+
+1.25%2A960+=+1200+
OK