There are some brown and yellow marbles in a box. If 2 brown marbles are removed from the box, the total number of marbles left will be 9 times the number of brown marbles left. If 9 yellow marbles are removed from the box, the total number of marbles left will be 4 times the number of brown marbles. How many marbles are there in the box?

	Case 1		Case 2
	Brown marbles	Yellow marbles	Brown marbles	Yellow marbles
Before	1 u + 2	8 u	1 p	3 p + 9
Change	- 2			- 9
After	1 u	8 u	1 p	3 p

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

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

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

8 u = 3 p + 9
8 u - 9 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 6 = 3 p --- (3)

(2) = (3)
8 u - 9 = 3 u + 6
8 u - 3 u = 6 + 9
5 u = 15

1 u = 15 ÷ 5 = 3

Number of marbles in the box
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 3) + 2
= 27 + 2
= 29

Answer(s): 29