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?
+313 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.
