There are some pink and grey balls in a box. If 9 pink balls are removed from the box, the total number of balls left will be 7 times the number of pink balls left. If 18 grey balls are removed from the box, the total number of balls left will be 3 times the number of pink balls. How many balls are there in the box?

	Case 1		Case 2
	Pink balls	Grey balls	Pink balls	Grey balls
Before	1 u + 9	6 u	1 p	2 p + 18
Change	- 9			- 18
After	1 u	6 u	1 p	2 p

Number of grey balls in the end for Case 1
= 7 u - 1 u
= 6 u

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

The number of pink 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 + 9 = 1 p --- (1)

6 u = 2 p + 18
6 u - 18 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 18 = 2 p --- (3)

(2) = (3)
6 u - 18 = 2 u + 18
6 u - 2 u = 18 + 18
4 u = 36

1 u = 36 ÷ 4 = 9

Number of balls in the box
= (1 u + 9) + 6 u
= 7 u + 9
= (7 x 9) + 9
= 63 + 9
= 72

Answer(s): 72