There are some red and pink marbles in a container. If 3 red marbles are removed from the container, the total number of marbles left will be 6 times the number of red marbles left. If 21 pink marbles are removed from the container, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the container?

	Case 1		Case 2
	Red marbles	Pink marbles	Red marbles	Pink marbles
Before	1 u + 3	5 u	1 p	2 p + 21
Change	- 3			- 21
After	1 u	5 u	1 p	2 p

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

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

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

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

5 u = 2 p + 21
5 u - 21 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
5 u - 21 = 2 u + 6
5 u - 2 u = 6 + 21
3 u = 27

1 u = 27 ÷ 3 = 9

Number of marbles in the container
= (1 u + 3) + 5 u
= 6 u + 3
= (6 x 9) + 3
= 54 + 3
= 57

Answer(s): 57