There are some grey and yellow balls in a box. If 2 grey balls are removed from the box, the total number of balls left will be 6 times the number of grey balls left. If 10 yellow balls are removed from the box, the total number of balls left will be 4 times the number of grey balls. How many balls are there in the box?

	Case 1		Case 2
	Grey balls	Yellow balls	Grey balls	Yellow balls
Before	1 u + 2	5 u	1 p	3 p + 10
Change	- 2			- 10
After	1 u	5 u	1 p	3 p

Number of yellow balls in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

1 u + 2 = 1 p --- (1)

5 u = 3 p + 10
5 u - 10 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 6 = 3 p --- (3)

(2) = (3)
5 u - 10 = 3 u + 6
5 u - 3 u = 6 + 10
2 u = 16

1 u = 16 ÷ 2 = 8

Number of balls in the box
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 8) + 2
= 48 + 2
= 50

Answer(s): 50