There are some green and grey balls in a container. If 4 green balls are removed from the container, the total number of balls left will be 9 times the number of green balls left. If 13 grey balls are removed from the container, the total number of balls left will be 4 times the number of green balls. How many balls are there in the container?

	Case 1		Case 2
	Green balls	Grey balls	Green balls	Grey balls
Before	1 u + 4	8 u	1 p	3 p + 13
Change	- 4			- 13
After	1 u	8 u	1 p	3 p

Number of grey balls in the end for Case 1
= 9 u - 1 u
= 8 u

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

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

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

8 u = 3 p + 13
8 u - 13 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 12 = 3 p --- (3)

(2) = (3)
8 u - 13 = 3 u + 12
8 u - 3 u = 12 + 13
5 u = 25

1 u = 25 ÷ 5 = 5

Number of balls in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 5) + 4
= 45 + 4
= 49

Answer(s): 49