There are some grey and green beads in a box. If 2 grey beads are removed from the box, the total number of beads left will be 5 times the number of grey beads left. If 8 green beads are removed from the box, the total number of beads left will be 3 times the number of grey beads. How many beads are there in the box?

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

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

Number of grey beads in the end for Case 2
= 3 p - 1 p
= 2 p

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

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

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

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
4 u - 8 = 2 u + 4
4 u - 2 u = 4 + 8
2 u = 12

1 u = 12 ÷ 2 = 6

Number of beads in the box
= (1 u + 2) + 4 u
= 5 u + 2
= (5 x 6) + 2
= 30 + 2
= 32

Answer(s): 32