Dylan, Wesley and Jeremy had a total of 97 cards. The ratio of Wesley's cards to Jeremy's cards was 4 : 7 at first. Dylan and Wesley each gave away ¹₂ of their cards. Given that the three boys had 73 cards left, how many cards did Dylan have at first?

	Dylan	Wesley	Jeremy	Total
Comparing Wesley and Jeremy at first		4 u	7 u
Before	2 p	2x2 = 4 u	7 u	97
Change	- 1 p	-1x2 = - 2 u		- 24
After	1 p	1x2 = 2 u	7 u	73

Total number of cards that Dylan and Wesley gave away
= 97 - 73
= 24

The number of cards that Wesley had at first is repeated.  Make the number of cards that Wesley had at first the same.  LCM of 4 and 2 is 4.

1 p + 2 u = 97 - 73
1 p + 2 u = 24
1 p = 24 - 2 u --- (1)

1 p + 2 u + 7 u = 73
1 p + 9 u = 73
1 p = 73 - 9 u --- (2)

(1) = (2)
24 - 2 u = 73 - 9 u
9 u - 2 u = 73 - 24
9 u - 2 u = 49
7 u = 49

1 u = 49 ÷ 7 = 7

Substitute 1 u = 7 into (1).
1 p = 24 - 2 u
1 p = 24 - 2 x 7
1 p = 24 - 14

1 p = 10

Number of cards that Dylan had at first
= 2 p
= 2 x 10
= 20

Answer(s): 20