There are some white and green balls in a box. If 8 white balls are removed from the box, the total number of balls left will be 9 times the number of white balls left. If 2 green balls are removed from the box, the total number of balls left will be 3 times the number of white balls. How many balls are there in the box?

	Case 1		Case 2
	White balls	Green balls	White balls	Green balls
Before	1 u + 8	8 u	1 p	2 p + 2
Change	- 8			- 2
After	1 u	8 u	1 p	2 p

Number of green balls in the end for Case 1
= 9 u - 1 u
= 8 u

Number of white balls in the end for Case 2
= 3 p - 1 p
= 2 p

The number of white balls at first is the same for Case 1 and Case 2.
The number of green balls at first is also the same for Case 1 and Case 2.

1 u + 8 = 1 p --- (1)

8 u = 2 p + 2
8 u - 2 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
8 u - 2 = 2 u + 16
8 u - 2 u = 16 + 2
6 u = 18

1 u = 18 ÷ 6 = 3

Number of balls in the box
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 3) + 8
= 27 + 8
= 35

Answer(s): 35