There are some grey and white marbles in a box. If 2 grey marbles are removed from the box, the total number of marbles left will be 8 times the number of grey marbles left. If 42 white marbles are removed from the box, the total number of marbles left will be 4 times the number of grey marbles. How many marbles are there in the box?

	Case 1		Case 2
	Grey marbles	White marbles	Grey marbles	White marbles
Before	1 u + 2	7 u	1 p	3 p + 42
Change	- 2			- 42
After	1 u	7 u	1 p	3 p

Number of white marbles in the end for Case 1
= 8 u - 1 u
= 7 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 white marbles at first is also the same for Case 1 and Case 2.

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

7 u = 3 p + 42
7 u - 42 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 6 = 3 p --- (3)

(2) = (3)
7 u - 42 = 3 u + 6
7 u - 3 u = 6 + 42
4 u = 48

1 u = 48 ÷ 4 = 12

Number of marbles in the box
= (1 u + 2) + 7 u
= 8 u + 2
= (8 x 12) + 2
= 96 + 2
= 98

Answer(s): 98