There are some gold and black balls in a box. If 2 gold balls are removed from the box, the total number of balls left will be 5 times the number of gold balls left. If 6 black balls are removed from the box, the total number of balls left will be 4 times the number of gold balls. How many balls are there in the box?

	Case 1		Case 2
	Gold balls	Black balls	Gold balls	Black balls
Before	1 u + 2	4 u	1 p	3 p + 6
Change	- 2			- 6
After	1 u	4 u	1 p	3 p

Number of black balls in the end for Case 1
= 5 u - 1 u
= 4 u

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

The number of gold balls at first is the same for Case 1 and Case 2.
The number of black balls at first is also the same for Case 1 and Case 2.

1 u + 2 = 1 p --- (1)

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

Make p the same.

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

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

1 u = 12 ÷ 1 = 12

Number of balls in the box
= (1 u + 2) + 4 u
= 5 u + 2
= (5 x 12) + 2
= 60 + 2
= 62

Answer(s): 62