Penelope, Yoko and Risa had a total of 190 stickers. The ratio of Yoko's stickers to Risa's stickers was at first 6 : 7. After Penelope and Yoko each gave half of their stickers away, the 3 children had 137 stickers left. How many stickers did Penelope and Yoko have at first?

	Penelope	Yoko	Risa	Total
Before	2 p	6 u	7 u	190
Change	- 1 p	- 3 u		- 53
After	1 p	3 u	7 u	137

Number of stickers that Penelope and Yoko gave away
= 190 - 137
= 53

1 p + 3 u = 53
1 p = 53 - 3 u --- (1)

1 p + 3 u + 7 u = 137
1 p + 10 u = 137
1 p = 137 - 10 u --- (2)

(1) = (2)
53 - 3 u = 137 - 10 u
10 u - 3 u = 137 - 53
7 u = 84

1 u = 84 ÷ 7 = 12

From (1)
1 p = 53 - 3 u
1 p = 53 - 3 x 12

1 p = 53 - 36 = 17

Number of stickers that Penelope and Yoko had at first
= 2 p + 6 u
= 2 x 17 + 6 x 12
= 34 + 84
= 118

Answer(s): 118