Ian, Wesley and Perry had a total of 60 beads. The ratio of Wesley's beads to Perry's beads was 4 : 7 at first. Ian and Wesley each gave away ¹₂ of their beads. Given that the three boys had 44 beads left, how many beads did Ian have in the end?

	Ian	Wesley	Perry	Total
Comparing Wesley and Perry at first		4 u	7 u
Before	2 p	2x2 = 4 u	7 u	60
Change	- 1 p	-1x2 = - 2 u		- 16
After	1 p	1x2 = 2 u	7 u	44

Total number of beads that Ian and Wesley gave away
= 60 - 44
= 16

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

1 p + 2 u = 60 - 44
1 p + 2 u = 16
1 p = 16 - 2 u --- (1)

1 p + 2 u + 7 u = 44
1 p + 9 u = 44
1 p = 44 - 9 u --- (2)

(1) = (2)
16 - 2 u = 44 - 9 u
9 u - 2 u = 44 - 16
9 u - 2 u = 28
7 u = 28

1 u = 28 ÷ 7 = 4

Substitute 1 u = 4 into (1).
1 p = 16 - 2 u
1 p = 16 - 2 x 4
1 p = 16 - 8

1 p = 8

Number of beads that Ian had in the end
= 1 p
= 8

Answer(s): 8