There are some gold and green balls in a container. If 5 gold balls are removed from the container, the total number of balls left will be 7 times the number of gold balls left. If 22 green balls are removed from the container, the total number of balls left will be 3 times the number of gold balls. How many balls are there in the container?

	Case 1		Case 2
	Gold balls	Green balls	Gold balls	Green balls
Before	1 u + 5	6 u	1 p	2 p + 22
Change	- 5			- 22
After	1 u	6 u	1 p	2 p

Number of green balls in the end for Case 1
= 7 u - 1 u
= 6 u

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

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

1 u + 5 = 1 p --- (1)

6 u = 2 p + 22
6 u - 22 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 10 = 2 p --- (3)

(2) = (3)
6 u - 22 = 2 u + 10
6 u - 2 u = 10 + 22
4 u = 32

1 u = 32 ÷ 4 = 8

Number of balls in the container
= (1 u + 5) + 6 u
= 7 u + 5
= (7 x 8) + 5
= 56 + 5
= 61

Answer(s): 61