There are some silver and white marbles in a box. If 9 silver marbles are removed from the box, the total number of marbles left will be 6 times the number of silver marbles left. If 12 white marbles are removed from the box, the total number of marbles left will be 3 times the number of silver marbles. How many marbles are there in the box?

	Case 1		Case 2
	Silver marbles	White marbles	Silver marbles	White marbles
Before	1 u + 9	5 u	1 p	2 p + 12
Change	- 9			- 12
After	1 u	5 u	1 p	2 p

Number of white marbles in the end for Case 1
= 6 u - 1 u
= 5 u

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

The number of silver 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 + 9 = 1 p --- (1)

5 u = 2 p + 12
5 u - 12 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 12 = 2 u + 18
5 u - 2 u = 18 + 12
3 u = 30

1 u = 30 ÷ 3 = 10

Number of marbles in the box
= (1 u + 9) + 5 u
= 6 u + 9
= (6 x 10) + 9
= 60 + 9
= 69

Answer(s): 69