Xylia, Emma and Cathy had a total of 266 stickers. The ratio of Emma's stickers to Cathy's stickers was at first 12 : 7. After Xylia and Emma each gave half of their stickers away, the 3 children had 175 stickers left. How many stickers did Xylia and Cathy have at first?

	Xylia	Emma	Cathy	Total
Before	2 p	12 u	7 u	266
Change	- 1 p	- 6 u		- 91
After	1 p	6 u	7 u	175

Number of stickers that Xylia and Emma gave away
= 266 - 175
= 91

1 p + 6 u = 91
1 p = 91 - 6 u --- (1)

1 p + 6 u + 7 u = 175 
1 p + 13 u = 175
1 p = 175 - 13 u --- (2)

(1) = (2) 
91 - 6 u = 175 - 13 u 
13 u - 6 u = 175 - 91
7 u = 84

1 u = 84 ÷ 7 = 12

From (1)
1 p = 91 - 6 u
1 p = 91 - 6 x 12

1 p = 91 - 72 = 19

Number of stickers that Xylia and Cathy had at first
= 2 p + 7 u
= 2 x 19 + 7 x 12
= 38 + 84
= 122

Answer(s): 122