There are some white and green marbles in a box. If 8 white marbles are removed from the box, the total number of marbles left will be 8 times the number of white marbles left. If 29 green marbles are removed from the box, the total number of marbles left will be 3 times the number of white marbles. How many marbles are there in the box?

	Case 1		Case 2
	White marbles	Green marbles	White marbles	Green marbles
Before	1 u + 8	7 u	1 p	2 p + 29
Change	- 8			- 29
After	1 u	7 u	1 p	2 p

Number of green marbles in the end for Case 1
= 8 u - 1 u
= 7 u

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

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

1 u + 8 = 1 p --- (1)

7 u = 2 p + 29
7 u - 29 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
7 u - 29 = 2 u + 16
7 u - 2 u = 16 + 29
5 u = 45

1 u = 45 ÷ 5 = 9

Number of marbles in the box
= (1 u + 8) + 7 u
= 8 u + 8
= (8 x 9) + 8
= 72 + 8
= 80

Answer(s): 80