There are some green and gold balls in a container. If 4 green balls are removed from the container, the total number of balls left will be 5 times the number of green balls left. If 8 gold balls are removed from the container, the total number of balls left will be 3 times the number of green balls. How many balls are there in the container?

	Case 1		Case 2
	Green balls	Gold balls	Green balls	Gold balls
Before	1 u + 4	4 u	1 p	2 p + 8
Change	- 4			- 8
After	1 u	4 u	1 p	2 p

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

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

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

1 u + 4 = 1 p --- (1)

4 u = 2 p + 8
4 u - 8 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
4 u - 8 = 2 u + 8
4 u - 2 u = 8 + 8
2 u = 16

1 u = 16 ÷ 2 = 8

Number of balls in the container
= (1 u + 4) + 4 u
= 5 u + 4
= (5 x 8) + 4
= 40 + 4
= 44

Answer(s): 44