There are some grey and purple 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 16 purple marbles are removed from the container, the total number of marbles left will be 3 times the number of grey marbles. How many marbles are there in the container?

	Case 1		Case 2
	Grey marbles	Purple marbles	Grey marbles	Purple marbles
Before	1 u + 6	6 u	1 p	2 p + 16
Change	- 6			- 16
After	1 u	6 u	1 p	2 p

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

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

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

6 u = 2 p + 16
6 u - 16 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 12 = 2 p --- (3)

(2) = (3)
6 u - 16 = 2 u + 12
6 u - 2 u = 12 + 16
4 u = 28

1 u = 28 ÷ 4 = 7

Number of marbles in the container
= (1 u + 6) + 6 u
= 7 u + 6
= (7 x 7) + 6
= 49 + 6
= 55

Answer(s): 55