There are some black and pink marbles in a box. If 3 black marbles are removed from the box, the total number of marbles left will be 8 times the number of black marbles left. If 6 pink marbles are removed from the box, the total number of marbles left will be 5 times the number of black marbles. How many marbles are there in the box?

	Case 1		Case 2
	Black marbles	Pink marbles	Black marbles	Pink marbles
Before	1 u + 3	7 u	1 p	4 p + 6
Change	- 3			- 6
After	1 u	7 u	1 p	4 p

Number of pink marbles in the end for Case 1
= 8 u - 1 u
= 7 u

Number of black marbles in the end for Case 2
= 5 p - 1 p
= 4 p

The number of black 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 + 3 = 1 p --- (1)

7 u = 4 p + 6
7 u - 6 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 12 = 4 p --- (3)

(2) = (3)
7 u - 6 = 4 u + 12
7 u - 4 u = 12 + 6
3 u = 18

1 u = 18 ÷ 3 = 6

Number of marbles in the box
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 6) + 3
= 48 + 3
= 51

Answer(s): 51