There are some red and black marbles in a container. If 2 red marbles are removed from the container, the total number of marbles left will be 9 times the number of red marbles left. If 32 black marbles are removed from the container, the total number of marbles left will be 5 times the number of red marbles. How many marbles are there in the container?

	Case 1		Case 2
	Red marbles	Black marbles	Red marbles	Black marbles
Before	1 u + 2	8 u	1 p	4 p + 32
Change	- 2			- 32
After	1 u	8 u	1 p	4 p

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

Number of red marbles in the end for Case 2
= 5 p - 1 p
= 4 p

The number of red 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)

8 u = 4 p + 32
8 u - 32 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 8 = 4 p --- (3)

(2) = (3)
8 u - 32 = 4 u + 8
8 u - 4 u = 8 + 32
4 u = 40

1 u = 40 ÷ 4 = 10

Number of marbles in the container
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 10) + 2
= 90 + 2
= 92

Answer(s): 92