There are some green and yellow marbles in a box. If 9 green marbles are removed from the box, the total number of marbles left will be 6 times the number of green marbles left. If 6 yellow marbles are removed from the box, the total number of marbles left will be 3 times the number of green marbles. How many marbles are there in the box?

	Case 1		Case 2
	Green marbles	Yellow marbles	Green marbles	Yellow marbles
Before	1 u + 9	5 u	1 p	2 p + 6
Change	- 9			- 6
After	1 u	5 u	1 p	2 p

Number of yellow marbles in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

1 u + 9 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 18 = 2 p --- (3)

(2) = (3)
5 u - 6 = 2 u + 18
5 u - 2 u = 18 + 6
3 u = 24

1 u = 24 ÷ 3 = 8

Number of marbles in the box
= (1 u + 9) + 5 u
= 6 u + 9
= (6 x 8) + 9
= 48 + 9
= 57

Answer(s): 57