There are some black and yellow balls in a box. If 8 black balls are removed from the box, the total number of balls left will be 7 times the number of black balls left. If 20 yellow 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	Yellow balls	Black balls	Yellow balls
Before	1 u + 8	6 u	1 p	2 p + 20
Change	- 8			- 20
After	1 u	6 u	1 p	2 p

Number of yellow balls in the end for Case 1
= 7 u - 1 u
= 6 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 yellow balls at first is also the same for Case 1 and Case 2.

1 u + 8 = 1 p --- (1)

6 u = 2 p + 20
6 u - 20 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
6 u - 20 = 2 u + 16
6 u - 2 u = 16 + 20
4 u = 36

1 u = 36 ÷ 4 = 9

Number of balls in the box
= (1 u + 8) + 6 u
= 7 u + 8
= (7 x 9) + 8
= 63 + 8
= 71

Answer(s): 71