There are some grey and green beads in a box. If 3 grey beads are removed from the box, the total number of beads left will be 8 times the number of grey beads left. If 54 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 + 3	7 u	1 p	2 p + 54
Change	- 3			- 54
After	1 u	7 u	1 p	2 p

Number of green beads in the end for Case 1
= 8 u - 1 u
= 7 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 + 3 = 1 p --- (1)

7 u = 2 p + 54
7 u - 54 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
7 u - 54 = 2 u + 6
7 u - 2 u = 6 + 54
5 u = 60

1 u = 60 ÷ 5 = 12

Number of beads in the box
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 12) + 3
= 96 + 3
= 99

Answer(s): 99