There are some grey and green marbles in a container. If 6 grey marbles are removed from the container, the total number of marbles left will be 7 times the number of grey marbles left. If 18 green marbles are removed from the container, the total number of marbles left will be 4 times the number of grey marbles. How many marbles are there in the container?

	Case 1		Case 2
	Grey marbles	Green marbles	Grey marbles	Green marbles
Before	1 u + 6	6 u	1 p	3 p + 18
Change	- 6			- 18
After	1 u	6 u	1 p	3 p

Number of green marbles in the end for Case 1
= 7 u - 1 u
= 6 u

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

The number of grey 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 + 6 = 1 p --- (1)

6 u = 3 p + 18
6 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 18 = 3 p --- (3)

(2) = (3)
6 u - 18 = 3 u + 18
6 u - 3 u = 18 + 18
3 u = 36

1 u = 36 ÷ 3 = 12

Number of marbles in the container
= (1 u + 6) + 6 u
= 7 u + 6
= (7 x 12) + 6
= 84 + 6
= 90

Answer(s): 90