There are some black and purple balls in a box. If 9 black balls are removed from the box, the total number of balls left will be 9 times the number of black balls left. If 36 purple 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	Purple balls	Black balls	Purple balls
Before	1 u + 9	8 u	1 p	2 p + 36
Change	- 9			- 36
After	1 u	8 u	1 p	2 p

Number of purple 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 purple balls at first is also the same for Case 1 and Case 2.

1 u + 9 = 1 p --- (1)

8 u = 2 p + 36
8 u - 36 = 2 p --- (2)

Make p the same.

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

(2) = (3)
8 u - 36 = 2 u + 18
8 u - 2 u = 18 + 36
6 u = 54

1 u = 54 ÷ 6 = 9

Number of balls in the box
= (1 u + 9) + 8 u
= 9 u + 9
= (9 x 9) + 9
= 81 + 9
= 90

Answer(s): 90