There are some yellow and purple balls in a container. If 2 yellow balls are removed from the container, the total number of balls left will be 7 times the number of yellow balls left. If 6 purple balls are removed from the container, the total number of balls left will be 4 times the number of yellow balls. How many balls are there in the container?

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

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

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

The number of yellow 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 + 2 = 1 p --- (1)

6 u = 3 p + 6
6 u - 6 = 3 p --- (2)

Make p the same.

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

(2) = (3)
6 u - 6 = 3 u + 6
6 u - 3 u = 6 + 6
3 u = 12

1 u = 12 ÷ 3 = 4

Number of balls in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 4) + 2
= 28 + 2
= 30

Answer(s): 30