
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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July 2nd, 2018, 07:43 PM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 310 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 updown cycle, the price of a painting decreased by 441. after a second updown cycle, the painting was sold for 1944.81 . What was the original price of the painting? Solution: (A441)(1+x/100)(1x/100)=1944.81 >(A441)(1x/100)2=1944.81 But here there are two unknowns A and X, so how to proceed from here ? 
July 2nd, 2018, 08:40 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,530 Thanks: 1750 
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, 08:58 PM  #3 
Senior Member Joined: Aug 2014 From: India Posts: 310 Thanks: 1  
July 3rd, 2018, 04:20 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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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