There are some black and grey marbles in a container. If 4 black marbles are removed from the container, the total number of marbles left will be 9 times the number of black marbles left. If 8 grey marbles are removed from the container, the total number of marbles left will be 5 times the number of black marbles. How many marbles are there in the container?

	Case 1		Case 2
	Black marbles	Grey marbles	Black marbles	Grey marbles
Before	1 u + 4	8 u	1 p	4 p + 8
Change	- 4			- 8
After	1 u	8 u	1 p	4 p

Number of grey marbles in the end for Case 1
= 9 u - 1 u
= 8 u

Number of black marbles in the end for Case 2
= 5 p - 1 p
= 4 p

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

1 u + 4 = 1 p --- (1)

8 u = 4 p + 8
8 u - 8 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 16 = 4 p --- (3)

(2) = (3)
8 u - 8 = 4 u + 16
8 u - 4 u = 16 + 8
4 u = 24

1 u = 24 ÷ 4 = 6

Number of marbles in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 6) + 4
= 54 + 4
= 58

Answer(s): 58