Penelope, Nicole and Gwen had a total of 182 coins. The ratio of Nicole's coins to Gwen's coins was at first 6 : 7. After Penelope and Nicole each gave half of their coins away, the 3 children had 133 coins left. How many coins did Penelope and Nicole have at first?

	Penelope	Nicole	Gwen	Total
Before	2 p	6 u	7 u	182
Change	- 1 p	- 3 u		- 49
After	1 p	3 u	7 u	133

Number of coins that Penelope and Nicole gave away
= 182 - 133
= 49

1 p + 3 u = 49
1 p = 49 - 3 u --- (1)

1 p + 3 u + 7 u = 133
1 p + 10 u = 133
1 p = 133 - 10 u --- (2)

(1) = (2)
49 - 3 u = 133 - 10 u
10 u - 3 u = 133 - 49
7 u = 84

1 u = 84 ÷ 7 = 12

From (1)
1 p = 49 - 3 u
1 p = 49 - 3 x 12

1 p = 49 - 36 = 13

Number of coins that Penelope and Nicole had at first
= 2 p + 6 u
= 2 x 13 + 6 x 12
= 26 + 84
= 110

Answer(s): 110