There are some yellow and brown balls in a container. If 6 yellow balls are removed from the container, the total number of balls left will be 6 times the number of yellow balls left. If 6 brown balls are removed from the container, the total number of balls left will be 4 times the number of yellow balls. How many balls are there in the container?

	Case 1		Case 2
	Yellow balls	Brown balls	Yellow balls	Brown balls
Before	1 u + 6	5 u	1 p	3 p + 6
Change	- 6			- 6
After	1 u	5 u	1 p	3 p

Number of brown balls in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

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

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

Make p the same.

(1)_x3
3 u + 18 = 3 p --- (3)

(2) = (3)
5 u - 6 = 3 u + 18
5 u - 3 u = 18 + 6
2 u = 24

1 u = 24 ÷ 2 = 12

Number of balls in the container
= (1 u + 6) + 5 u
= 6 u + 6
= (6 x 12) + 6
= 72 + 6
= 78

Answer(s): 78