There are some red and brown balls in a box. If 4 red balls are removed from the box, the total number of balls left will be 9 times the number of red balls left. If 40 brown balls are removed from the box, the total number of balls left will be 3 times the number of red balls. How many balls are there in the box?

	Case 1		Case 2
	Red balls	Brown balls	Red balls	Brown balls
Before	1 u + 4	8 u	1 p	2 p + 40
Change	- 4			- 40
After	1 u	8 u	1 p	2 p

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

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

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

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

8 u = 2 p + 40
8 u - 40 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
8 u - 40 = 2 u + 8
8 u - 2 u = 8 + 40
6 u = 48

1 u = 48 ÷ 6 = 8

Number of balls in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 8) + 4
= 72 + 4
= 76

Answer(s): 76