There are some white and brown marbles in a box. If 10 white marbles are removed from the box, the total number of marbles left will be 9 times the number of white marbles left. If 5 brown marbles are removed from the box, the total number of marbles left will be 4 times the number of white marbles. How many marbles are there in the box?

	Case 1		Case 2
	White marbles	Brown marbles	White marbles	Brown marbles
Before	1 u + 10	8 u	1 p	3 p + 5
Change	- 10			- 5
After	1 u	8 u	1 p	3 p

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

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

The number of white 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 + 10 = 1 p --- (1)

8 u = 3 p + 5
8 u - 5 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 30 = 3 p --- (3)

(2) = (3)
8 u - 5 = 3 u + 30
8 u - 3 u = 30 + 5
5 u = 35

1 u = 35 ÷ 5 = 7

Number of marbles in the box
= (1 u + 10) + 8 u
= 9 u + 10
= (9 x 7) + 10
= 63 + 10
= 73

Answer(s): 73