There are some purple and black marbles in a container. If 10 purple marbles are removed from the container, the total number of marbles left will be 8 times the number of purple marbles left. If 2 black marbles are removed from the container, the total number of marbles left will be 4 times the number of purple marbles. How many marbles are there in the container?

	Case 1		Case 2
	Purple marbles	Black marbles	Purple marbles	Black marbles
Before	1 u + 10	7 u	1 p	3 p + 2
Change	- 10			- 2
After	1 u	7 u	1 p	3 p

Number of black marbles in the end for Case 1
= 8 u - 1 u
= 7 u

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

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

7 u = 3 p + 2
7 u - 2 = 3 p --- (2)

Make p the same.

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

(2) = (3)
7 u - 2 = 3 u + 30
7 u - 3 u = 30 + 2
4 u = 32

1 u = 32 ÷ 4 = 8

Number of marbles in the container
= (1 u + 10) + 7 u
= 8 u + 10
= (8 x 8) + 10
= 64 + 10
= 74

Answer(s): 74