There are some black and white balls in a container. If 3 black balls are removed from the container, the total number of balls left will be 8 times the number of black balls left. If 9 white balls are removed from the container, the total number of balls left will be 6 times the number of black balls. How many balls are there in the container?

	Case 1		Case 2
	Black balls	White balls	Black balls	White balls
Before	1 u + 3	7 u	1 p	5 p + 9
Change	- 3			- 9
After	1 u	7 u	1 p	5 p

Number of white balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of black balls in the end for Case 2
= 6 p - 1 p
= 5 p

The number of black 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 + 3 = 1 p --- (1)

7 u = 5 p + 9
7 u - 9 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 15 = 5 p --- (3)

(2) = (3)
7 u - 9 = 5 u + 15
7 u - 5 u = 15 + 9
2 u = 24

1 u = 24 ÷ 2 = 12

Number of balls in the container
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 12) + 3
= 96 + 3
= 99

Answer(s): 99