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Amy folded a total of 516 paper cranes and stars for a charity fair on the 1st day. After selling 5/6 of the number of cranes and 2/3 of the number of stars, she folded another 72 cranes and 84 stars for sale on the 2nd day. Now the ratio of the number of cranes to the number of stars became 3:4. How many paper stars did she fold on the 1st day?

 Jan 17, 2022
edited by Guest  Jan 17, 2022
edited by Guest  Jan 17, 2022
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Let x be the number of paper cranes 

      y be the number of paper stars

(1)  x + y = 516 => x = 516 - y

(2)    2nd day cranes :

              x - 5/6x + 72 = 1/6x + 72

        2nd day stars : 

               y - 2/3y + 84 = 1/3y + 84

          (1/6x + 72)/1/3y + 84 = 3/4

           2/3x + 288 = y + 252

              x + 3/2 (288) = 3/2(y + 262)

              x = 3/2y + 378 - 432

              x = 3/2y - 5$

By comparison x = x

     3/2y - 54 = 516 - y

     3/2y + y = 516 + 54

     5/2y = 570

          y = 228

Amy folded 228 paper stars on the first day.

 Jan 20, 2022

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