There are some gold and blue marbles in a box. If 10 gold marbles are removed from the box, the total number of marbles left will be 8 times the number of gold marbles left. If 6 blue marbles are removed from the box, the total number of marbles left will be 4 times the number of gold marbles. How many marbles are there in the box?

	Case 1		Case 2
	Gold marbles	Blue marbles	Gold marbles	Blue marbles
Before	1 u + 10	7 u	1 p	3 p + 6
Change	- 10			- 6
After	1 u	7 u	1 p	3 p

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

Number of gold marbles in the end for Case 2
= 4 p - 1 p
= 3 p

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

1 u + 10 = 1 p --- (1)

7 u = 3 p + 6
7 u - 6 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 30 = 3 p --- (3)

(2) = (3)
7 u - 6 = 3 u + 30
7 u - 3 u = 30 + 6
4 u = 36

1 u = 36 ÷ 4 = 9

Number of marbles in the box
= (1 u + 10) + 7 u
= 8 u + 10
= (8 x 9) + 10
= 72 + 10
= 82

Answer(s): 82