There are some green and gold beads in a container. If 6 green beads are removed from the container, the total number of beads left will be 5 times the number of green beads left. If 6 gold beads are removed from the container, the total number of beads left will be 3 times the number of green beads. How many beads are there in the container?

	Case 1		Case 2
	Green beads	Gold beads	Green beads	Gold beads
Before	1 u + 6	4 u	1 p	2 p + 6
Change	- 6			- 6
After	1 u	4 u	1 p	2 p

Number of gold beads in the end for Case 1
= 5 u - 1 u
= 4 u

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

The number of green 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 + 6 = 1 p --- (1)

4 u = 2 p + 6
4 u - 6 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 12 = 2 p --- (3)

(2) = (3)
4 u - 6 = 2 u + 12
4 u - 2 u = 12 + 6
2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads in the container
= (1 u + 6) + 4 u
= 5 u + 6
= (5 x 9) + 6
= 45 + 6
= 51

Answer(s): 51