SOLUTION: 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 t

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 t      Log On


   

Question 1204644: 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?
Answer by ikleyn(52800) About Me  (Show Source):
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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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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 %283%2F2%29x.
       %283%2F2%29x-x = %281%2F2%29x 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 %284%2F3%29x.
       %284%2F3%29x-x = %281%2F3%29x 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 + %281%2F2%29x + %281%2F3%29x = 330.


Simplify and find x

    x + x%2F2 + x%2F3 = 330

    %286x%29%2F6 + %283x%29%2F6 + %282x%29%2F6 = 330

    %2811x%29%2F6 = 330

    x = 330%2A%286%2F11%29 = 30*6 = 180.

 
Each shop sold 180 lanterns.    ANSWER

Solved.