There are some yellow and grey balls in a container. If 5 yellow balls are removed from the container, the total number of balls left will be 8 times the number of yellow balls left. If 16 grey balls are removed from the container, the total number of balls left will be 5 times the number of yellow balls. How many balls are there in the container?

	Case 1		Case 2
	Yellow balls	Grey balls	Yellow balls	Grey balls
Before	1 u + 5	7 u	1 p	4 p + 16
Change	- 5			- 16
After	1 u	7 u	1 p	4 p

Number of grey balls in the end for Case 1
= 8 u - 1 u
= 7 u

Number of yellow balls in the end for Case 2
= 5 p - 1 p
= 4 p

The number of yellow 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 + 5 = 1 p --- (1)

7 u = 4 p + 16
7 u - 16 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 20 = 4 p --- (3)

(2) = (3)
7 u - 16 = 4 u + 20
7 u - 4 u = 20 + 16
3 u = 36

1 u = 36 ÷ 3 = 12

Number of balls in the container
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 12) + 5
= 96 + 5
= 101

Answer(s): 101