There are some purple and yellow marbles in a container. If 7 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 yellow 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	Yellow marbles	Purple marbles	Yellow marbles
Before	1 u + 7	6 u	1 p	3 p + 6
Change	- 7			- 6
After	1 u	6 u	1 p	3 p

Number of yellow 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 yellow marbles at first is also the same for Case 1 and Case 2.

1 u + 7 = 1 p --- (1)

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

Make p the same.

(1)_x3
3 u + 21 = 3 p --- (3)

(2) = (3)
6 u - 6 = 3 u + 21
6 u - 3 u = 21 + 6
3 u = 27

1 u = 27 ÷ 3 = 9

Number of marbles in the container
= (1 u + 7) + 6 u
= 7 u + 7
= (7 x 9) + 7
= 63 + 7
= 70

Answer(s): 70