There are some red and pink marbles in a box. If 8 red marbles are removed from the box, the total number of marbles left will be 6 times the number of red marbles left. If 20 pink marbles are removed from the box, the total number of marbles left will be 3 times the number of red marbles. How many marbles are there in the box?

	Case 1		Case 2
	Red marbles	Pink marbles	Red marbles	Pink marbles
Before	1 u + 8	5 u	1 p	2 p + 20
Change	- 8			- 20
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 + 8 = 1 p --- (1)

5 u = 2 p + 20
5 u - 20 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
5 u - 20 = 2 u + 16
5 u - 2 u = 16 + 20
3 u = 36

1 u = 36 ÷ 3 = 12

Number of marbles in the box
= (1 u + 8) + 5 u
= 6 u + 8
= (6 x 12) + 8
= 72 + 8
= 80

Answer(s): 80