There are some grey and white beads in a box. If 2 grey beads are removed from the box, the total number of beads left will be 6 times the number of grey beads left. If 18 white beads are removed from the box, the total number of beads left will be 4 times the number of grey beads. How many beads are there in the box?

	Case 1		Case 2
	Grey beads	White beads	Grey beads	White beads
Before	1 u + 2	5 u	1 p	3 p + 18
Change	- 2			- 18
After	1 u	5 u	1 p	3 p

Number of white beads in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

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

5 u = 3 p + 18
5 u - 18 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 6 = 3 p --- (3)

(2) = (3)
5 u - 18 = 3 u + 6
5 u - 3 u = 6 + 18
2 u = 24

1 u = 24 ÷ 2 = 12

Number of beads in the box
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 12) + 2
= 72 + 2
= 74

Answer(s): 74