Lee, Eric and Wesley had a total of 62 marbles. The ratio of Eric's marbles to Wesley's marbles was 2 : 5 at first. Lee and Eric each gave away ¹₂ of their marbles. Given that the three boys had 51 marbles left, how many marbles did Lee have at first?

	Lee	Eric	Wesley	Total
Comparing Eric and Wesley at first		2 u	5 u
Before	2 p	2x1 = 2 u	5 u	62
Change	- 1 p	-1x1 = - 1 u		- 11
After	1 p	1x1 = 1 u	5 u	51

Total number of marbles that Lee and Eric gave away
= 62 - 51
= 11

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

1 p + 1 u = 62 - 51
1 p + 1 u = 11
1 p = 11 - 1 u --- (1)

1 p + 1 u + 5 u = 51
1 p + 6 u = 51
1 p = 51 - 6 u --- (2)

(1) = (2)
11 - 1 u = 51 - 6 u
6 u - 1 u = 51 - 11
6 u - 1 u = 40
5 u = 40

1 u = 40 ÷ 5 = 8

Substitute 1 u = 8 into (1).
1 p = 11 - 1 u
1 p = 11 - 1 x 8
1 p = 11 - 8

1 p = 3

Number of marbles that Lee had at first
= 2 p
= 2 x 3
= 6

Answer(s): 6