There are some blue and purple balls in a box. If 2 blue balls are removed from the box, the total number of balls left will be 8 times the number of blue balls left. If 14 purple balls are removed from the box, the total number of balls left will be 6 times the number of blue balls. How many balls are there in the box?

	Case 1		Case 2
	Blue balls	Purple balls	Blue balls	Purple balls
Before	1 u + 2	7 u	1 p	5 p + 14
Change	- 2			- 14
After	1 u	7 u	1 p	5 p

Number of purple balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of blue balls in the end for Case 2
= 6 p - 1 p
= 5 p

The number of blue 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)

7 u = 5 p + 14
7 u - 14 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 10 = 5 p --- (3)

(2) = (3)
7 u - 14 = 5 u + 10
7 u - 5 u = 10 + 14
2 u = 24

1 u = 24 ÷ 2 = 12

Number of balls in the box
= (1 u + 2) + 7 u
= 8 u + 2
= (8 x 12) + 2
= 96 + 2
= 98

Answer(s): 98