There are some gold and purple marbles in a container. If 8 gold marbles are removed from the container, the total number of marbles left will be 6 times the number of gold marbles left. If 14 purple marbles are removed from the container, the total number of marbles left will be 3 times the number of gold marbles. How many marbles are there in the container?

	Case 1		Case 2
	Gold marbles	Purple marbles	Gold marbles	Purple marbles
Before	1 u + 8	5 u	1 p	2 p + 14
Change	- 8			- 14
After	1 u	5 u	1 p	2 p

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

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

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

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

5 u = 2 p + 14
5 u - 14 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 14 = 2 u + 16
5 u - 2 u = 16 + 14
3 u = 30

1 u = 30 ÷ 3 = 10

Number of marbles in the container
= (1 u + 8) + 5 u
= 6 u + 8
= (6 x 10) + 8
= 60 + 8
= 68

Answer(s): 68