There are some yellow and brown marbles in a box. If 9 yellow marbles are removed from the box, the total number of marbles left will be 5 times the number of yellow marbles left. If 2 brown marbles are removed from the box, the total number of marbles left will be 3 times the number of yellow marbles. How many marbles are there in the box?

	Case 1		Case 2
	Yellow marbles	Brown marbles	Yellow marbles	Brown marbles
Before	1 u + 9	4 u	1 p	2 p + 2
Change	- 9			- 2
After	1 u	4 u	1 p	2 p

Number of brown marbles in the end for Case 1
= 5 u - 1 u
= 4 u

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

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

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

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

Make p the same.

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

(2) = (3)
4 u - 2 = 2 u + 18
4 u - 2 u = 18 + 2
2 u = 20

1 u = 20 ÷ 2 = 10

Number of marbles in the box
= (1 u + 9) + 4 u
= 5 u + 9
= (5 x 10) + 9
= 50 + 9
= 59

Answer(s): 59