There are some yellow and blue marbles in a container. If 3 yellow marbles are removed from the container, the total number of marbles left will be 9 times the number of yellow marbles left. If 6 blue marbles are removed from the container, the total number of marbles left will be 4 times the number of yellow marbles. How many marbles are there in the container?

	Case 1		Case 2
	Yellow marbles	Blue marbles	Yellow marbles	Blue marbles
Before	1 u + 3	8 u	1 p	3 p + 6
Change	- 3			- 6
After	1 u	8 u	1 p	3 p

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

Number of yellow marbles in the end for Case 2
= 4 p - 1 p
= 3 p

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

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

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

Make p the same.

(1)_x3
3 u + 9 = 3 p --- (3)

(2) = (3)
8 u - 6 = 3 u + 9
8 u - 3 u = 9 + 6
5 u = 15

1 u = 15 ÷ 5 = 3

Number of marbles in the container
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 3) + 3
= 27 + 3
= 30

Answer(s): 30