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 July 2nd, 2018, 08:43 PM #1 Senior Member   Joined: Aug 2014 From: India Posts: 343 Thanks: 1 how to proceed from here ? The owner of an art shop conducts the business in the following manner. Every once in a while he raises his prices by x%, then a while later he reduces all the new prices by x%. After one such up-down cycle, the price of a painting decreased by 441. after a second up-down cycle, the painting was sold for 1944.81 . What was the original price of the painting? Solution: (A-441)(1+x/100)(1-x/100)=1944.81 -->(A-441)(1-x/100)2=1944.81 But here there are two unknowns A and X, so how to proceed from here ?
 July 2nd, 2018, 09:40 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,285 Thanks: 1968 If original price is y, and u = (1 + x/100)(1 - x/100), yu = y - 441 and yu² = 1944.81, so y²u² = y² - 882y + 441² = 1944.81y Solving that gives y = 70.56 or 2756.25. As y has to exceed 441, its value is 2756.25. If you're interested, x = 40.
July 2nd, 2018, 09:58 PM   #3
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Joined: Aug 2014
From: India

Posts: 343
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Quote:
 Originally Posted by skipjack yu² = 1944.81,
How you got yu^2 = 1944.81?

 July 3rd, 2018, 05:20 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 896 The problem says that the merchant increases prices by x percent: if the original price is y then the new price is y(1+ x/100). He then decreases the price by x percent: the final price after such a "cycle" is y(1+ x/100)(1- x/100). To simplify the writing, skipjack defined u to be "(1+ x/100)(1- x/100)". So after one "cycle" the new price is yu. But the problem said "after two cycles" the price was 1944.81. Each cycle multiplies y by u so after two cycles, the price is (yu)(u)= yu^2= 1944.81.

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