There are some blue and green marbles in a box. If 8 blue marbles are removed from the box, the total number of marbles left will be 9 times the number of blue marbles left. If 31 green marbles are removed from the box, the total number of marbles left will be 4 times the number of blue marbles. How many marbles are there in the box?

	Case 1		Case 2
	Blue marbles	Green marbles	Blue marbles	Green marbles
Before	1 u + 8	8 u	1 p	3 p + 31
Change	- 8			- 31
After	1 u	8 u	1 p	3 p

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

Number of blue marbles in the end for Case 2
= 4 p - 1 p
= 3 p

The number of blue 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)

8 u = 3 p + 31
8 u - 31 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 24 = 3 p --- (3)

(2) = (3)
8 u - 31 = 3 u + 24
8 u - 3 u = 24 + 31
5 u = 55

1 u = 55 ÷ 5 = 11

Number of marbles in the box
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 11) + 8
= 99 + 8
= 107

Answer(s): 107