There are some red and purple marbles in a container. If 10 red marbles are removed from the container, the total number of marbles left will be 6 times the number of red marbles left. If 10 purple marbles are removed from the container, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the container?

	Case 1		Case 2
	Red marbles	Purple marbles	Red marbles	Purple marbles
Before	1 u + 10	5 u	1 p	2 p + 10
Change	- 10			- 10
After	1 u	5 u	1 p	2 p

Number of purple marbles in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

1 u + 10 = 1 p --- (1)

5 u = 2 p + 10
5 u - 10 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 20 = 2 p --- (3)

(2) = (3)
5 u - 10 = 2 u + 20
5 u - 2 u = 20 + 10
3 u = 30

1 u = 30 ÷ 3 = 10

Number of marbles in the container
= (1 u + 10) + 5 u
= 6 u + 10
= (6 x 10) + 10
= 60 + 10
= 70

Answer(s): 70