There are some gold and black marbles in a container. If 2 gold marbles are removed from the container, the total number of marbles left will be 7 times the number of gold marbles left. If 24 black marbles are removed from the container, the total number of marbles left will be 3 times the number of gold marbles. How many marbles are there in the container?

	Case 1		Case 2
	Gold marbles	Black marbles	Gold marbles	Black marbles
Before	1 u + 2	6 u	1 p	2 p + 24
Change	- 2			- 24
After	1 u	6 u	1 p	2 p

Number of black marbles in the end for Case 1
= 7 u - 1 u
= 6 u

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

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

1 u + 2 = 1 p --- (1)

6 u = 2 p + 24
6 u - 24 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
6 u - 24 = 2 u + 4
6 u - 2 u = 4 + 24
4 u = 28

1 u = 28 ÷ 4 = 7

Number of marbles in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 7) + 2
= 49 + 2
= 51

Answer(s): 51