There are some silver and grey balls in a box. If 6 silver balls are removed from the box, the total number of balls left will be 9 times the number of silver balls left. If 8 grey balls are removed from the box, the total number of balls left will be 5 times the number of silver balls. How many balls are there in the box?

	Case 1		Case 2
	Silver balls	Grey balls	Silver balls	Grey balls
Before	1 u + 6	8 u	1 p	4 p + 8
Change	- 6			- 8
After	1 u	8 u	1 p	4 p

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

Number of silver balls in the end for Case 2
= 5 p - 1 p
= 4 p

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

1 u + 6 = 1 p --- (1)

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

Make p the same.

(1)_x4
4 u + 24 = 4 p --- (3)

(2) = (3)
8 u - 8 = 4 u + 24
8 u - 4 u = 24 + 8
4 u = 32

1 u = 32 ÷ 4 = 8

Number of balls in the box
= (1 u + 6) + 8 u
= 9 u + 6
= (9 x 8) + 6
= 72 + 6
= 78

Answer(s): 78