There are some purple and gold marbles in a container. If 10 purple marbles are removed from the container, the total number of marbles left will be 7 times the number of purple marbles left. If 6 gold 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	Gold marbles	Purple marbles	Gold marbles
Before	1 u + 10	6 u	1 p	3 p + 6
Change	- 10			- 6
After	1 u	6 u	1 p	3 p

Number of gold marbles in the end for Case 1
= 7 u - 1 u
= 6 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 gold marbles at first is also the same for Case 1 and Case 2.

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

6 u = 3 p + 6
6 u - 6 = 3 p --- (2)

Make p the same.

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

(2) = (3)
6 u - 6 = 3 u + 30
6 u - 3 u = 30 + 6
3 u = 36

1 u = 36 ÷ 3 = 12

Number of marbles in the container
= (1 u + 10) + 6 u
= 7 u + 10
= (7 x 12) + 10
= 84 + 10
= 94

Answer(s): 94