There are some red and blue balls in a container. If 9 red balls are removed from the container, the total number of balls left will be 9 times the number of red balls left. If 12 blue balls are removed from the container, the total number of balls left will be 5 times the number of red balls. How many balls are there in the container?

	Case 1		Case 2
	Red balls	Blue balls	Red balls	Blue balls
Before	1 u + 9	8 u	1 p	4 p + 12
Change	- 9			- 12
After	1 u	8 u	1 p	4 p

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

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

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

1 u + 9 = 1 p --- (1)

8 u = 4 p + 12
8 u - 12 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 36 = 4 p --- (3)

(2) = (3)
8 u - 12 = 4 u + 36
8 u - 4 u = 36 + 12
4 u = 48

1 u = 48 ÷ 4 = 12

Number of balls in the container
= (1 u + 9) + 8 u
= 9 u + 9
= (9 x 12) + 9
= 108 + 9
= 117

Answer(s): 117