There are some black and yellow balls in a box. If 3 black balls are removed from the box, the total number of balls left will be 6 times the number of black balls left. If 3 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 + 3	5 u	1 p	2 p + 3
Change	- 3			- 3
After	1 u	5 u	1 p	2 p

Number of yellow balls in the end for Case 1
= 6 u - 1 u
= 5 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 + 3 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
5 u - 3 = 2 u + 6
5 u - 2 u = 6 + 3
3 u = 9

1 u = 9 ÷ 3 = 3

Number of balls in the box
= (1 u + 3) + 5 u
= 6 u + 3
= (6 x 3) + 3
= 18 + 3
= 21

Answer(s): 21