There are some red and white marbles in a box. If 3 red marbles are removed from the box, the total number of marbles left will be 9 times the number of red marbles left. If 30 white marbles are removed from the box, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the box?

	Case 1		Case 2
	Red marbles	White marbles	Red marbles	White marbles
Before	1 u + 3	8 u	1 p	2 p + 30
Change	- 3			- 30
After	1 u	8 u	1 p	2 p

Number of white marbles in the end for Case 1
= 9 u - 1 u
= 8 u

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

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

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

8 u = 2 p + 30
8 u - 30 = 2 p --- (2)

Make p the same.

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

(2) = (3)
8 u - 30 = 2 u + 6
8 u - 2 u = 6 + 30
6 u = 36

1 u = 36 ÷ 6 = 6

Number of marbles in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 6) + 3
= 54 + 3
= 57

Answer(s): 57