There are some purple and white marbles in a container. If 2 purple marbles are removed from the container, the total number of marbles left will be 7 times the number of purple marbles left. If 16 white marbles are removed from the container, the total number of marbles left will be 3 times the number of purple marbles. How many marbles are there in the container?

	Case 1		Case 2
	Purple marbles	White marbles	Purple marbles	White marbles
Before	1 u + 2	6 u	1 p	2 p + 16
Change	- 2			- 16
After	1 u	6 u	1 p	2 p

Number of white marbles in the end for Case 1
= 7 u - 1 u
= 6 u

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

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

1 u + 2 = 1 p --- (1)

6 u = 2 p + 16
6 u - 16 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
6 u - 16 = 2 u + 4
6 u - 2 u = 4 + 16
4 u = 20

1 u = 20 ÷ 4 = 5

Number of marbles in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 5) + 2
= 35 + 2
= 37

Answer(s): 37