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Dane, Enzo and Fraser shared some game cards. Dane had 2/5 of what Enzo

had. Enzo had 6 times of what Fraser had. After Dane lost some of his game 

cards in school, he had 1/7 of the total game cards that Enzo and Fraser had.

The three boys had 280 game cards altogether in the end.

(a)      What was the ratio of Dane's share to Enzo's share to Fraser's share at

           first?

(b)      How many game cards did Dane lose in school?

 Dec 16, 2021
 #1
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Let Dane has D, Enzo had E and

Fraser has F game cars at first.

(a) According to the question,

                  D = 2/5E     and E = 6F

             => D = \( {2\over 5}\) * 6F = \( {12 \over 5}F\)

Now the ratio of Dane's share to Enzo's share

       to Fraser's  share is

        D : E : F = 12/5 K: 6F : F

                      = 12/5 : 6 : 1

                      = 12 : 30 : 5

 

(b) Let Dane lost 'y' game cards in school.

    From the first         part (a)   Let Dane had 12x,

    Enzo had 30x and Fraser had 5x game card at

    first.

    According to the question,

           12x - y = 1/7 (30x + 5x)

         => 12x - y = 1/7 * 355x

         => 12x - y = 5x

            => y = 7x    ------- (1)

     Also given three boys had 250 game cards altogether

            in the end.

        So,   (12x - y) + 300x + 5x = 250

           => (12x - 7x) + 35x = 250

           => 5x + 35x = 280

           => 40x = 280

            => x = 7

Dane lost y = 7x = 7 * 7 = 49 game cards in school.

 Dec 17, 2021

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