There are some brown and gold beads in a container. If 2 brown beads are removed from the container, the total number of beads left will be 6 times the number of brown beads left. If 2 gold beads are removed from the container, the total number of beads left will be 5 times the number of brown beads. How many beads are there in the container?

	Case 1		Case 2
	Brown beads	Gold beads	Brown beads	Gold beads
Before	1 u + 2	5 u	1 p	4 p + 2
Change	- 2			- 2
After	1 u	5 u	1 p	4 p

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

Number of brown beads in the end for Case 2
= 5 p - 1 p
= 4 p

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

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

5 u = 4 p + 2
5 u - 2 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 8 = 4 p --- (3)

(2) = (3)
5 u - 2 = 4 u + 8
5 u - 4 u = 8 + 2
1 u = 10

1 u = 10 ÷ 1 = 10

Number of beads in the container
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 10) + 2
= 60 + 2
= 62

Answer(s): 62