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July 2nd, 2018, 07:43 PM   #1
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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


But here there are two unknowns A and X, so how to proceed from here ?
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July 2nd, 2018, 08:40 PM   #2
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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.
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July 2nd, 2018, 08:58 PM   #3
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Originally Posted by skipjack View Post
yu² = 1944.81,
How you got yu^2 = 1944.81?
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July 3rd, 2018, 04:20 AM   #4
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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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