There are some gold and yellow balls in a container. If 9 gold balls are removed from the container, the total number of balls left will be 6 times the number of gold balls left. If 15 yellow 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	Yellow balls	Gold balls	Yellow balls
Before	1 u + 9	5 u	1 p	2 p + 15
Change	- 9			- 15
After	1 u	5 u	1 p	2 p

Number of yellow balls in the end for Case 1
= 6 u - 1 u
= 5 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 yellow balls at first is also the same for Case 1 and Case 2.

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

5 u = 2 p + 15
5 u - 15 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 18 = 2 p --- (3)

(2) = (3)
5 u - 15 = 2 u + 18
5 u - 2 u = 18 + 15
3 u = 33

1 u = 33 ÷ 3 = 11

Number of balls in the container
= (1 u + 9) + 5 u
= 6 u + 9
= (6 x 11) + 9
= 66 + 9
= 75

Answer(s): 75