There are some black and grey beads in a box. If 8 black beads are removed from the box, the total number of beads left will be 9 times the number of black beads left. If 11 grey beads are removed from the box, the total number of beads left will be 4 times the number of black beads. How many beads are there in the box?

	Case 1		Case 2
	Black beads	Grey beads	Black beads	Grey beads
Before	1 u + 8	8 u	1 p	3 p + 11
Change	- 8			- 11
After	1 u	8 u	1 p	3 p

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

Number of black beads in the end for Case 2
= 4 p - 1 p
= 3 p

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

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

8 u = 3 p + 11
8 u - 11 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 24 = 3 p --- (3)

(2) = (3)
8 u - 11 = 3 u + 24
8 u - 3 u = 24 + 11
5 u = 35

1 u = 35 ÷ 5 = 7

Number of beads in the box
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 7) + 8
= 63 + 8
= 71

Answer(s): 71