There are some black and green marbles in a container. If 2 black marbles are removed from the container, the total number of marbles left will be 5 times the number of black marbles left. If 6 green marbles are removed from the container, the total number of marbles left will be 3 times the number of black marbles. How many marbles are there in the container?

	Case 1		Case 2
	Black marbles	Green marbles	Black marbles	Green marbles
Before	1 u + 2	4 u	1 p	2 p + 6
Change	- 2			- 6
After	1 u	4 u	1 p	2 p

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

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

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

1 u + 2 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
4 u - 6 = 2 u + 4
4 u - 2 u = 4 + 6
2 u = 10

1 u = 10 ÷ 2 = 5

Number of marbles in the container
= (1 u + 2) + 4 u
= 5 u + 2
= (5 x 5) + 2
= 25 + 2
= 27

Answer(s): 27