There are some white and gold marbles in a container. If 8 white marbles are removed from the container, the total number of marbles left will be 5 times the number of white marbles left. If 6 gold marbles are removed from the container, the total number of marbles left will be 3 times the number of white marbles. How many marbles are there in the container?

	Case 1		Case 2
	White marbles	Gold marbles	White marbles	Gold marbles
Before	1 u + 8	4 u	1 p	2 p + 6
Change	- 8			- 6
After	1 u	4 u	1 p	2 p

Number of gold marbles in the end for Case 1
= 5 u - 1 u
= 4 u

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

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

1 u + 8 = 1 p --- (1)

4 u = 2 p + 6
4 u - 6 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
4 u - 6 = 2 u + 16
4 u - 2 u = 16 + 6
2 u = 22

1 u = 22 ÷ 2 = 11

Number of marbles in the container
= (1 u + 8) + 4 u
= 5 u + 8
= (5 x 11) + 8
= 55 + 8
= 63

Answer(s): 63