There are some blue and grey marbles in a container. If 7 blue marbles are removed from the container, the total number of marbles left will be 6 times the number of blue marbles left. If 10 grey marbles are removed from the container, the total number of marbles left will be 3 times the number of blue marbles. How many marbles are there in the container?

	Case 1		Case 2
	Blue marbles	Grey marbles	Blue marbles	Grey marbles
Before	1 u + 7	5 u	1 p	2 p + 10
Change	- 7			- 10
After	1 u	5 u	1 p	2 p

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

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

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

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

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

Make p the same.

(1)_x2
2 u + 14 = 2 p --- (3)

(2) = (3)
5 u - 10 = 2 u + 14
5 u - 2 u = 14 + 10
3 u = 24

1 u = 24 ÷ 3 = 8

Number of marbles in the container
= (1 u + 7) + 5 u
= 6 u + 7
= (6 x 8) + 7
= 48 + 7
= 55

Answer(s): 55