There are some yellow and brown marbles in a container. If 8 yellow marbles are removed from the container, the total number of marbles left will be 6 times the number of yellow marbles left. If 2 brown marbles are removed from the container, the total number of marbles left will be 3 times the number of yellow marbles. How many marbles are there in the container?

	Case 1		Case 2
	Yellow marbles	Brown marbles	Yellow marbles	Brown marbles
Before	1 u + 8	5 u	1 p	2 p + 2
Change	- 8			- 2
After	1 u	5 u	1 p	2 p

Number of brown marbles in the end for Case 1
= 6 u - 1 u
= 5 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 + 8 = 1 p --- (1)

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

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
5 u - 2 = 2 u + 16
5 u - 2 u = 16 + 2
3 u = 18

1 u = 18 ÷ 3 = 6

Number of marbles in the container
= (1 u + 8) + 5 u
= 6 u + 8
= (6 x 6) + 8
= 36 + 8
= 44

Answer(s): 44