Jade, Tina and Tiffany had a total of 230 marbles. The ratio of Tina's marbles to Tiffany's marbles was at first 10 : 9. After Jade and Tina each gave half of their marbles away, the 3 children had 160 marbles left. How many marbles did Jade and Tina have at first?

	Jade	Tina	Tiffany	Total
Before	2 p	10 u	9 u	230
Change	- 1 p	- 5 u		- 70
After	1 p	5 u	9 u	160

Number of marbles that Jade and Tina gave away
= 230 - 160
= 70

1 p + 5 u = 70
1 p = 70 - 5 u --- (1)

1 p + 5 u + 9 u = 160
1 p + 14 u = 160
1 p = 160 - 14 u --- (2)

(1) = (2)
70 - 5 u = 160 - 14 u
14 u - 5 u = 160 - 70
9 u = 90

1 u = 90 ÷ 9 = 10

From (1)
1 p = 70 - 5 u
1 p = 70 - 5 x 10

1 p = 70 - 50 = 20

Number of marbles that Jade and Tina had at first
= 2 p + 10 u
= 2 x 20 + 10 x 10
= 40 + 90
= 130

Answer(s): 130