There are some pink and silver marbles in a box. If 2 pink marbles are removed from the box, the total number of marbles left will be 8 times the number of pink marbles left. If 34 silver marbles are removed from the box, the total number of marbles left will be 4 times the number of pink marbles. How many marbles are there in the box?

	Case 1		Case 2
	Pink marbles	Silver marbles	Pink marbles	Silver marbles
Before	1 u + 2	7 u	1 p	3 p + 34
Change	- 2			- 34
After	1 u	7 u	1 p	3 p

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

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

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

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

7 u = 3 p + 34
7 u - 34 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 6 = 3 p --- (3)

(2) = (3)
7 u - 34 = 3 u + 6
7 u - 3 u = 6 + 34
4 u = 40

1 u = 40 ÷ 4 = 10

Number of marbles in the box
= (1 u + 2) + 7 u
= 8 u + 2
= (8 x 10) + 2
= 80 + 2
= 82

Answer(s): 82