There are some white and red 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 18 red balls are removed from the box, the total number of balls left will be 4 times the number of white balls. How many balls are there in the box?

	Case 1		Case 2
	White balls	Red balls	White balls	Red balls
Before	1 u + 4	8 u	1 p	3 p + 18
Change	- 4			- 18
After	1 u	8 u	1 p	3 p

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

Number of white balls in the end for Case 2
= 4 p - 1 p
= 3 p

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

1 u + 4 = 1 p --- (1)

8 u = 3 p + 18
8 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 12 = 3 p --- (3)

(2) = (3)
8 u - 18 = 3 u + 12
8 u - 3 u = 12 + 18
5 u = 30

1 u = 30 ÷ 5 = 6

Number of balls in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 6) + 4
= 54 + 4
= 58

Answer(s): 58