Anna, Pamela and Natalie had a total of 127 marbles. The ratio of Pamela's marbles to Natalie's marbles was at first 12 : 7. After Anna and Pamela each gave half of their marbles away, the 3 children had 81 marbles left. How many marbles did Anna and Pamela have at first?

	Anna	Pamela	Natalie	Total
Before	2 p	12 u	7 u	127
Change	- 1 p	- 6 u		- 46
After	1 p	6 u	7 u	81

Number of marbles that Anna and Pamela gave away
= 127 - 81
= 46

1 p + 6 u = 46
1 p = 46 - 6 u --- (1)

1 p + 6 u + 7 u = 81
1 p + 13 u = 81
1 p = 81 - 13 u --- (2)

(1) = (2)
46 - 6 u = 81 - 13 u
13 u - 6 u = 81 - 46
7 u = 35

1 u = 35 ÷ 7 = 5

From (1)
1 p = 46 - 6 u
1 p = 46 - 6 x 5

1 p = 46 - 30 = 16

Number of marbles that Anna and Pamela had at first
= 2 p + 12 u
= 2 x 16 + 12 x 5
= 32 + 35
= 67

Answer(s): 67