There are some blue and white marbles in a container. If 6 blue marbles are removed from the container, the total number of marbles left will be 9 times the number of blue marbles left. If 20 white marbles are removed from the container, the total number of marbles left will be 5 times the number of blue marbles. How many marbles are there in the container?

	Case 1		Case 2
	Blue marbles	White marbles	Blue marbles	White marbles
Before	1 u + 6	8 u	1 p	4 p + 20
Change	- 6			- 20
After	1 u	8 u	1 p	4 p

Number of white marbles in the end for Case 1
= 9 u - 1 u
= 8 u

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

The number of blue 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 + 6 = 1 p --- (1)

8 u = 4 p + 20
8 u - 20 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 24 = 4 p --- (3)

(2) = (3)
8 u - 20 = 4 u + 24
8 u - 4 u = 24 + 20
4 u = 44

1 u = 44 ÷ 4 = 11

Number of marbles in the container
= (1 u + 6) + 8 u
= 9 u + 6
= (9 x 11) + 6
= 99 + 6
= 105

Answer(s): 105