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# A simple percent problem.

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The original price for a pair of shoes was increased by 150%, and then this new price was decreased by 75%. By what percent must the current price be increased to return to the original price?

Just curious to see your solutions

Sep 6, 2018

#1
+100588
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Let P  be the original price

The new  price  is   P(1.5)(.25)  = .375 P

So....to return to the original price.....we must increase this new price by

1 / .375  ≈  2.66 ≈  266%

Sep 6, 2018
edited by CPhill  Sep 6, 2018
#2
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Assume the original price =\$100

An increase of 150% means: 150/100 + 1 =2.50

S0, the original price of \$100 x 2.50 =\$250 - the new price after 150% increase. Remember that 100% increase will double the price from \$100 to \$200. So, 150% will increase the price to \$250.

\$250 x 25% =\$62.50 - The new price after being discounted by 75%.

So, to go from \$62.50 to \$100, the percentage must go up by: \$100/\$62.50 =60% to get to the original price of \$100, because \$62.5 x 1.6 =\$100.

Sep 6, 2018