There are some gold and grey balls in a container. If 6 gold balls are removed from the container, the total number of balls left will be 8 times the number of gold balls left. If 12 grey balls are removed from the container, the total number of balls left will be 5 times the number of gold balls. How many balls are there in the container?

	Case 1		Case 2
	Gold balls	Grey balls	Gold balls	Grey balls
Before	1 u + 6	7 u	1 p	4 p + 12
Change	- 6			- 12
After	1 u	7 u	1 p	4 p

Number of grey balls in the end for Case 1
= 8 u - 1 u
= 7 u

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

The number of gold 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)

7 u = 4 p + 12
7 u - 12 = 4 p --- (2)

Make p the same.

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

(2) = (3)
7 u - 12 = 4 u + 24
7 u - 4 u = 24 + 12
3 u = 36

1 u = 36 ÷ 3 = 12

Number of balls in the container
= (1 u + 6) + 7 u
= 8 u + 6
= (8 x 12) + 6
= 96 + 6
= 102

Answer(s): 102