There are some white and purple marbles in a box. If 2 white marbles are removed from the box, the total number of marbles left will be 7 times the number of white marbles left. If 6 purple marbles are removed from the box, the total number of marbles left will be 5 times the number of white marbles. How many marbles are there in the box?

	Case 1		Case 2
	White marbles	Purple marbles	White marbles	Purple marbles
Before	1 u + 2	6 u	1 p	4 p + 6
Change	- 2			- 6
After	1 u	6 u	1 p	4 p

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

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

The number of white 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 + 2 = 1 p --- (1)

6 u = 4 p + 6
6 u - 6 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 8 = 4 p --- (3)

(2) = (3)
6 u - 6 = 4 u + 8
6 u - 4 u = 8 + 6
2 u = 14

1 u = 14 ÷ 2 = 7

Number of marbles in the box
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 7) + 2
= 49 + 2
= 51

Answer(s): 51