There are some gold and silver marbles in a container. If 3 gold marbles are removed from the container, the total number of marbles left will be 6 times the number of gold marbles left. If 3 silver marbles are removed from the container, the total number of marbles left will be 4 times the number of gold marbles. How many marbles are there in the container?

	Case 1		Case 2
	Gold marbles	Silver marbles	Gold marbles	Silver marbles
Before	1 u + 3	5 u	1 p	3 p + 3
Change	- 3			- 3
After	1 u	5 u	1 p	3 p

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

Number of gold marbles in the end for Case 2
= 4 p - 1 p
= 3 p

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

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

5 u = 3 p + 3
5 u - 3 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 9 = 3 p --- (3)

(2) = (3)
5 u - 3 = 3 u + 9
5 u - 3 u = 9 + 3
2 u = 12

1 u = 12 ÷ 2 = 6

Number of marbles in the container
= (1 u + 3) + 5 u
= 6 u + 3
= (6 x 6) + 3
= 36 + 3
= 39

Answer(s): 39