There are some purple and black marbles in a box. If 6 purple marbles are removed from the box, the total number of marbles left will be 8 times the number of purple marbles left. If 28 black marbles are removed from the box, the total number of marbles left will be 3 times the number of purple marbles. How many marbles are there in the box?

	Case 1		Case 2
	Purple marbles	Black marbles	Purple marbles	Black marbles
Before	1 u + 6	7 u	1 p	2 p + 28
Change	- 6			- 28
After	1 u	7 u	1 p	2 p

Number of black marbles in the end for Case 1
= 8 u - 1 u
= 7 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 black marbles at first is also the same for Case 1 and Case 2.

1 u + 6 = 1 p --- (1)

7 u = 2 p + 28
7 u - 28 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 12 = 2 p --- (3)

(2) = (3)
7 u - 28 = 2 u + 12
7 u - 2 u = 12 + 28
5 u = 40

1 u = 40 ÷ 5 = 8

Number of marbles in the box
= (1 u + 6) + 7 u
= 8 u + 6
= (8 x 8) + 6
= 64 + 6
= 70

Answer(s): 70