There are some green and purple balls in a box. If 3 green balls are removed from the box, the total number of balls left will be 9 times the number of green balls left. If 12 purple balls are removed from the box, the total number of balls left will be 5 times the number of green balls. How many balls are there in the box?

	Case 1		Case 2
	Green balls	Purple balls	Green balls	Purple balls
Before	1 u + 3	8 u	1 p	4 p + 12
Change	- 3			- 12
After	1 u	8 u	1 p	4 p

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

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

The number of green 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 + 3 = 1 p --- (1)

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

Make p the same.

(1)_x4
4 u + 12 = 4 p --- (3)

(2) = (3)
8 u - 12 = 4 u + 12
8 u - 4 u = 12 + 12
4 u = 24

1 u = 24 ÷ 4 = 6

Number of balls in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 6) + 3
= 54 + 3
= 57

Answer(s): 57