There are some black and purple balls in a container. If 6 black balls are removed from the container, the total number of balls left will be 8 times the number of black balls left. If 3 purple balls are removed from the container, the total number of balls left will be 3 times the number of black balls. How many balls are there in the container?

	Case 1		Case 2
	Black balls	Purple balls	Black balls	Purple balls
Before	1 u + 6	7 u	1 p	2 p + 3
Change	- 6			- 3
After	1 u	7 u	1 p	2 p

Number of purple balls in the end for Case 1
= 8 u - 1 u
= 7 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 + 6 = 1 p --- (1)

7 u = 2 p + 3
7 u - 3 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 12 = 2 p --- (3)

(2) = (3)
7 u - 3 = 2 u + 12
7 u - 2 u = 12 + 3
5 u = 15

1 u = 15 ÷ 5 = 3

Number of balls in the container
= (1 u + 6) + 7 u
= 8 u + 6
= (8 x 3) + 6
= 24 + 6
= 30

Answer(s): 30