There are some red and gold balls in a box. If 3 red balls are removed from the box, the total number of balls left will be 9 times the number of red balls left. If 24 gold balls are removed from the box, the total number of balls left will be 3 times the number of red balls. How many balls are there in the box?

	Case 1		Case 2
	Red balls	Gold balls	Red balls	Gold balls
Before	1 u + 3	8 u	1 p	2 p + 24
Change	- 3			- 24
After	1 u	8 u	1 p	2 p

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

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

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

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

8 u = 2 p + 24
8 u - 24 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
8 u - 24 = 2 u + 6
8 u - 2 u = 6 + 24
6 u = 30

1 u = 30 ÷ 6 = 5

Number of balls in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 5) + 3
= 45 + 3
= 48

Answer(s): 48