Glen, Jenson and Oliver had a total of 120 cards. The ratio of Jenson's cards to Oliver's cards was 2 : 7 at first. Glen and Jenson each gave away ¹₂ of their cards. Given that the three boys had 102 cards left, how many cards did Glen have at first?

	Glen	Jenson	Oliver	Total
Comparing Jenson and Oliver at first		2 u	7 u
Before	2 p	2x1 = 2 u	7 u	120
Change	- 1 p	-1x1 = - 1 u		- 18
After	1 p	1x1 = 1 u	7 u	102

Total number of cards that Glen and Jenson gave away
= 120 - 102
= 18

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

1 p + 1 u = 120 - 102
1 p + 1 u = 18
1 p = 18 - 1 u --- (1)

1 p + 1 u + 7 u = 102
1 p + 8 u = 102
1 p = 102 - 8 u --- (2)

(1) = (2)
18 - 1 u = 102 - 8 u
8 u - 1 u = 102 - 18
8 u - 1 u = 84
7 u = 84

1 u = 84 ÷ 7 = 12

Substitute 1 u = 12 into (1).
1 p = 18 - 1 u
1 p = 18 - 1 x 12
1 p = 18 - 12

1 p = 6

Number of cards that Glen had at first
= 2 p
= 2 x 6
= 12

Answer(s): 12