There are some pink and gold marbles in a box. If 2 pink marbles are removed from the box, the total number of marbles left will be 9 times the number of pink marbles left. If 8 gold marbles are removed from the box, the total number of marbles left will be 6 times the number of pink marbles. How many marbles are there in the box?

	Case 1		Case 2
	Pink marbles	Gold marbles	Pink marbles	Gold marbles
Before	1 u + 2	8 u	1 p	5 p + 8
Change	- 2			- 8
After	1 u	8 u	1 p	5 p

Number of gold marbles in the end for Case 1
= 9 u - 1 u
= 8 u

Number of pink marbles in the end for Case 2
= 6 p - 1 p
= 5 p

The number of pink marbles at first is the same for Case 1 and Case 2.
The number of gold marbles at first is also the same for Case 1 and Case 2.

1 u + 2 = 1 p --- (1)

8 u = 5 p + 8
8 u - 8 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 10 = 5 p --- (3)

(2) = (3)
8 u - 8 = 5 u + 10
8 u - 5 u = 10 + 8
3 u = 18

1 u = 18 ÷ 3 = 6

Number of marbles in the box
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 6) + 2
= 54 + 2
= 56

Answer(s): 56