There are some gold and grey beads in a container. If 2 gold beads are removed from the container, the total number of beads left will be 6 times the number of gold beads left. If 20 grey beads are removed from the container, the total number of beads left will be 3 times the number of gold beads. How many beads are there in the container?

	Case 1		Case 2
	Gold beads	Grey beads	Gold beads	Grey beads
Before	1 u + 2	5 u	1 p	2 p + 20
Change	- 2			- 20
After	1 u	5 u	1 p	2 p

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

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

The number of gold 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 + 2 = 1 p --- (1)

5 u = 2 p + 20
5 u - 20 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 20 = 2 u + 4
5 u - 2 u = 4 + 20
3 u = 24

1 u = 24 ÷ 3 = 8

Number of beads in the container
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 8) + 2
= 48 + 2
= 50

Answer(s): 50