There are some purple and blue marbles in a container. If 4 purple marbles are removed from the container, the total number of marbles left will be 7 times the number of purple marbles left. If 12 blue marbles are removed from the container, the total number of marbles left will be 3 times the number of purple marbles. How many marbles are there in the container?

	Case 1		Case 2
	Purple marbles	Blue marbles	Purple marbles	Blue marbles
Before	1 u + 4	6 u	1 p	2 p + 12
Change	- 4			- 12
After	1 u	6 u	1 p	2 p

Number of blue marbles in the end for Case 1
= 7 u - 1 u
= 6 u

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

The number of purple 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 + 4 = 1 p --- (1)

6 u = 2 p + 12
6 u - 12 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
6 u - 12 = 2 u + 8
6 u - 2 u = 8 + 12
4 u = 20

1 u = 20 ÷ 4 = 5

Number of marbles in the container
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 5) + 4
= 35 + 4
= 39

Answer(s): 39