There are some white and blue balls in a box. If 4 white balls are removed from the box, the total number of balls left will be 9 times the number of white balls left. If 24 blue balls are removed from the box, the total number of balls left will be 5 times the number of white balls. How many balls are there in the box?

	Case 1		Case 2
	White balls	Blue balls	White balls	Blue balls
Before	1 u + 4	8 u	1 p	4 p + 24
Change	- 4			- 24
After	1 u	8 u	1 p	4 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
= 5 p - 1 p
= 4 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 + 4 = 1 p --- (1)

8 u = 4 p + 24
8 u - 24 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 16 = 4 p --- (3)

(2) = (3)
8 u - 24 = 4 u + 16
8 u - 4 u = 16 + 24
4 u = 40

1 u = 40 ÷ 4 = 10

Number of balls in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 10) + 4
= 90 + 4
= 94

Answer(s): 94