There are some gold and purple marbles in a container. If 4 gold marbles are removed from the container, the total number of marbles left will be 5 times the number of gold marbles left. If 2 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 + 4	4 u	1 p	2 p + 2
Change	- 4			- 2
After	1 u	4 u	1 p	2 p

Number of purple marbles in the end for Case 1
= 5 u - 1 u
= 4 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 + 4 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
4 u - 2 = 2 u + 8
4 u - 2 u = 8 + 2
2 u = 10

1 u = 10 ÷ 2 = 5

Number of marbles in the container
= (1 u + 4) + 4 u
= 5 u + 4
= (5 x 5) + 4
= 25 + 4
= 29

Answer(s): 29