There are some silver and green marbles in a container. If 2 silver marbles are removed from the container, the total number of marbles left will be 7 times the number of silver marbles left. If 16 green marbles are removed from the container, the total number of marbles left will be 5 times the number of silver marbles. How many marbles are there in the container?

	Case 1		Case 2
	Silver marbles	Green marbles	Silver marbles	Green marbles
Before	1 u + 2	6 u	1 p	4 p + 16
Change	- 2			- 16
After	1 u	6 u	1 p	4 p

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

Number of silver marbles in the end for Case 2
= 5 p - 1 p
= 4 p

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

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

6 u = 4 p + 16
6 u - 16 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 8 = 4 p --- (3)

(2) = (3)
6 u - 16 = 4 u + 8
6 u - 4 u = 8 + 16
2 u = 24

1 u = 24 ÷ 2 = 12

Number of marbles in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 12) + 2
= 84 + 2
= 86

Answer(s): 86