Gillian, Cathy and Gwen had a total of 189 beads. The ratio of Cathy's beads to Gwen's beads was at first 4 : 9. After Gillian and Cathy each gave half of their beads away, the 3 children had 144 beads left. How many beads did Gillian and Cathy have at first?

	Gillian	Cathy	Gwen	Total
Before	2 p	4 u	9 u	189
Change	- 1 p	- 2 u		- 45
After	1 p	2 u	9 u	144

Number of beads that Gillian and Cathy gave away
= 189 - 144
= 45

1 p + 2 u = 45
1 p = 45 - 2 u --- (1)

1 p + 2 u + 9 u = 144
1 p + 11 u = 144
1 p = 144 - 11 u --- (2)

(1) = (2)
45 - 2 u = 144 - 11 u
11 u - 2 u = 144 - 45
9 u = 99

1 u = 99 ÷ 9 = 11

From (1)
1 p = 45 - 2 u
1 p = 45 - 2 x 11

1 p = 45 - 22 = 23

Number of beads that Gillian and Cathy had at first
= 2 p + 4 u
= 2 x 23 + 4 x 11
= 46 + 99
= 145

Answer(s): 145