There are some red and pink marbles in a container. If 4 red marbles are removed from the container, the total number of marbles left will be 7 times the number of red marbles left. If 8 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 + 4	6 u	1 p	2 p + 8
Change	- 4			- 8
After	1 u	6 u	1 p	2 p

Number of pink marbles in the end for Case 1
= 7 u - 1 u
= 6 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 + 4 = 1 p --- (1)

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

Make p the same.

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

(2) = (3)
6 u - 8 = 2 u + 8
6 u - 2 u = 8 + 8
4 u = 16

1 u = 16 ÷ 4 = 4

Number of marbles in the container
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 4) + 4
= 28 + 4
= 32

Answer(s): 32