There are some blue and purple marbles in a container. If 2 blue marbles are removed from the container, the total number of marbles left will be 5 times the number of blue marbles left. If 18 purple 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	Purple marbles	Blue marbles	Purple marbles
Before	1 u + 2	4 u	1 p	2 p + 18
Change	- 2			- 18
After	1 u	4 u	1 p	2 p

Number of purple marbles in the end for Case 1
= 5 u - 1 u
= 4 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 purple marbles at first is also the same for Case 1 and Case 2.

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

4 u = 2 p + 18
4 u - 18 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
4 u - 18 = 2 u + 4
4 u - 2 u = 4 + 18
2 u = 22

1 u = 22 ÷ 2 = 11

Number of marbles in the container
= (1 u + 2) + 4 u
= 5 u + 2
= (5 x 11) + 2
= 55 + 2
= 57

Answer(s): 57