There are some grey and purple marbles in a box. If 7 grey marbles are removed from the box, the total number of marbles left will be 6 times the number of grey marbles left. If 4 purple marbles are removed from the box, the total number of marbles left will be 3 times the number of grey marbles. How many marbles are there in the box?

	Case 1		Case 2
	Grey marbles	Purple marbles	Grey marbles	Purple marbles
Before	1 u + 7	5 u	1 p	2 p + 4
Change	- 7			- 4
After	1 u	5 u	1 p	2 p

Number of purple marbles in the end for Case 1
= 6 u - 1 u
= 5 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 + 7 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 14 = 2 p --- (3)

(2) = (3)
5 u - 4 = 2 u + 14
5 u - 2 u = 14 + 4
3 u = 18

1 u = 18 ÷ 3 = 6

Number of marbles in the box
= (1 u + 7) + 5 u
= 6 u + 7
= (6 x 6) + 7
= 36 + 7
= 43

Answer(s): 43