There are some green and white balls in a container. If 8 green balls are removed from the container, the total number of balls left will be 9 times the number of green balls left. If 4 white balls are removed from the container, the total number of balls left will be 5 times the number of green balls. How many balls are there in the container?

	Case 1		Case 2
	Green balls	White balls	Green balls	White balls
Before	1 u + 8	8 u	1 p	4 p + 4
Change	- 8			- 4
After	1 u	8 u	1 p	4 p

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

Number of green balls in the end for Case 2
= 5 p - 1 p
= 4 p

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

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

8 u = 4 p + 4
8 u - 4 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 32 = 4 p --- (3)

(2) = (3)
8 u - 4 = 4 u + 32
8 u - 4 u = 32 + 4
4 u = 36

1 u = 36 ÷ 4 = 9

Number of balls in the container
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 9) + 8
= 81 + 8
= 89

Answer(s): 89