There are some black and green beads in a box. If 2 black beads are removed from the box, the total number of beads left will be 8 times the number of black beads left. If 12 green beads are removed from the box, the total number of beads left will be 6 times the number of black beads. How many beads are there in the box?

	Case 1		Case 2
	Black beads	Green beads	Black beads	Green beads
Before	1 u + 2	7 u	1 p	5 p + 12
Change	- 2			- 12
After	1 u	7 u	1 p	5 p

Number of green beads in the end for Case 1
= 8 u - 1 u
= 7 u

Number of black beads in the end for Case 2
= 6 p - 1 p
= 5 p

The number of black 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)

7 u = 5 p + 12
7 u - 12 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 10 = 5 p --- (3)

(2) = (3)
7 u - 12 = 5 u + 10
7 u - 5 u = 10 + 12
2 u = 22

1 u = 22 ÷ 2 = 11

Number of beads in the box
= (1 u + 2) + 7 u
= 8 u + 2
= (8 x 11) + 2
= 88 + 2
= 90

Answer(s): 90