Sabrina, Kathy and Usha had a total of 81 marbles. The ratio of Kathy's marbles to Usha's marbles was at first 10 : 7. After Sabrina and Kathy each gave half of their marbles away, the 3 children had 51 marbles left. How many marbles did Sabrina and Kathy have at first?

	Sabrina	Kathy	Usha	Total
Before	2 p	10 u	7 u	81
Change	- 1 p	- 5 u		- 30
After	1 p	5 u	7 u	51

Number of marbles that Sabrina and Kathy gave away
= 81 - 51
= 30

1 p + 5 u = 30
1 p = 30 - 5 u --- (1)

1 p + 5 u + 7 u = 51
1 p + 12 u = 51
1 p = 51 - 12 u --- (2)

(1) = (2)
30 - 5 u = 51 - 12 u
12 u - 5 u = 51 - 30
7 u = 21

1 u = 21 ÷ 7 = 3

From (1)
1 p = 30 - 5 u
1 p = 30 - 5 x 3

1 p = 30 - 15 = 15

Number of marbles that Sabrina and Kathy had at first
= 2 p + 10 u
= 2 x 15 + 10 x 3
= 30 + 21
= 51

Answer(s): 51