There are some black and green balls in a box. If 4 black balls are removed from the box, the total number of balls left will be 9 times the number of black balls left. If 34 green balls are removed from the box, the total number of balls left will be 3 times the number of black balls. How many balls are there in the box?

	Case 1		Case 2
	Black balls	Green balls	Black balls	Green balls
Before	1 u + 4	8 u	1 p	2 p + 34
Change	- 4			- 34
After	1 u	8 u	1 p	2 p

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

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

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

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

8 u = 2 p + 34
8 u - 34 = 2 p --- (2)

Make p the same.

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

(2) = (3)
8 u - 34 = 2 u + 8
8 u - 2 u = 8 + 34
6 u = 42

1 u = 42 ÷ 6 = 7

Number of balls in the box
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 7) + 4
= 63 + 4
= 67

Answer(s): 67