Question 1204644
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Three shops sold the same number of lanterns during the lantern festival. 
Shop A sold 1/2 or its lanterns, Shop B sold 2/3 of its lanterns and 
Shop C sold 3/4 of its lanterns. If the three shops had a total of 330 lanterns left, 
how many lanterns did each shop sell?
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<pre>
Let x be the same number of lanterns sold in each shop.


Shop 1 sold 1/2 of its lanterns; this 1/2 is x; 
       hence, the original amount of lanterns in shop 1 was 2x.
       2x-x = x is the amount of lanterns remained in shop 1.



Shop 2 sold 2/3 of its lanterns; this 2/3 is x; 
       hence, the original amount of lanterns in shop 2 was {{{(3/2)x}}}.
       {{{(3/2)x-x}}} = {{{(1/2)x}}} is the amount of lanterns remained in shop 2.



Shop 3 sold 3/4 of its lanterns; this 3/4 is x; 
       hence, the original amount of lanterns in shop 3 was {{{(4/3)x}}}.
       {{{(4/3)x-x}}} = {{{(1/3)x}}} is the amount of lanterns remained in shop 3.



The three shops had a total of 330 lanterns left. It gives us this equation

    x + {{{(1/2)x}}} + {{{(1/3)x}}} = 330.


Simplify and find x

    x + {{{x/2}}} + {{{x/3}}} = 330

    {{{(6x)/6}}} + {{{(3x)/6}}} + {{{(2x)/6}}} = 330

    {{{(11x)/6}}} = 330

    x = {{{330*(6/11)}}} = 30*6 = 180.

 
Each shop sold 180 lanterns.    <U>ANSWER</U>
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Solved.