There are some green and pink beads in a box. If 8 green beads are removed from the box, the total number of beads left will be 9 times the number of green beads left. If 16 pink beads are removed from the box, the total number of beads left will be 5 times the number of green beads. How many beads are there in the box?

	Case 1		Case 2
	Green beads	Pink beads	Green beads	Pink beads
Before	1 u + 8	8 u	1 p	4 p + 16
Change	- 8			- 16
After	1 u	8 u	1 p	4 p

Number of pink beads in the end for Case 1
= 9 u - 1 u
= 8 u

Number of green beads in the end for Case 2
= 5 p - 1 p
= 4 p

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

1 u + 8 = 1 p --- (1)

8 u = 4 p + 16
8 u - 16 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 32 = 4 p --- (3)

(2) = (3)
8 u - 16 = 4 u + 32
8 u - 4 u = 32 + 16
4 u = 48

1 u = 48 ÷ 4 = 12

Number of beads in the box
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 12) + 8
= 108 + 8
= 116

Answer(s): 116