There are some silver and purple marbles in a box. If 5 silver marbles are removed from the box, the total number of marbles left will be 9 times the number of silver marbles left. If 5 purple marbles are removed from the box, the total number of marbles left will be 6 times the number of silver marbles. How many marbles are there in the box?

	Case 1		Case 2
	Silver marbles	Purple marbles	Silver marbles	Purple marbles
Before	1 u + 5	8 u	1 p	5 p + 5
Change	- 5			- 5
After	1 u	8 u	1 p	5 p

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

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

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

1 u + 5 = 1 p --- (1)

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

Make p the same.

(1)_x5
5 u + 25 = 5 p --- (3)

(2) = (3)
8 u - 5 = 5 u + 25
8 u - 5 u = 25 + 5
3 u = 30

1 u = 30 ÷ 3 = 10

Number of marbles in the box
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 10) + 5
= 90 + 5
= 95

Answer(s): 95