There are some grey and purple marbles in a box. If 5 grey marbles are removed from the box, the total number of marbles left will be 9 times the number of grey marbles left. If 24 purple marbles are removed from the box, the total number of marbles left will be 5 times the number of grey marbles. How many marbles are there in the box?

	Case 1		Case 2
	Grey marbles	Purple marbles	Grey marbles	Purple marbles
Before	1 u + 5	8 u	1 p	4 p + 24
Change	- 5			- 24
After	1 u	8 u	1 p	4 p

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

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

The number of grey 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 = 4 p + 24
8 u - 24 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 20 = 4 p --- (3)

(2) = (3)
8 u - 24 = 4 u + 20
8 u - 4 u = 20 + 24
4 u = 44

1 u = 44 ÷ 4 = 11

Number of marbles in the box
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 11) + 5
= 99 + 5
= 104

Answer(s): 104