There are some white and blue balls in a container. If 5 white balls are removed from the container, the total number of balls left will be 9 times the number of white balls left. If 8 blue balls are removed from the container, the total number of balls left will be 3 times the number of white balls. How many balls are there in the container?

	Case 1		Case 2
	White balls	Blue balls	White balls	Blue balls
Before	1 u + 5	8 u	1 p	2 p + 8
Change	- 5			- 8
After	1 u	8 u	1 p	2 p

Number of blue 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 blue balls at first is also the same for Case 1 and Case 2.

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

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

Make p the same.

(1)_x2
2 u + 10 = 2 p --- (3)

(2) = (3)
8 u - 8 = 2 u + 10
8 u - 2 u = 10 + 8
6 u = 18

1 u = 18 ÷ 6 = 3

Number of balls in the container
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 3) + 5
= 27 + 5
= 32

Answer(s): 32