There are some green and pink beads in a container. If 6 green beads are removed from the container, the total number of beads left will be 6 times the number of green beads left. If 21 pink 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	Pink beads	Green beads	Pink beads
Before	1 u + 6	5 u	1 p	2 p + 21
Change	- 6			- 21
After	1 u	5 u	1 p	2 p

Number of pink beads in the end for Case 1
= 6 u - 1 u
= 5 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 pink beads at first is also the same for Case 1 and Case 2.

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

5 u = 2 p + 21
5 u - 21 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 21 = 2 u + 12
5 u - 2 u = 12 + 21
3 u = 33

1 u = 33 ÷ 3 = 11

Number of beads in the container
= (1 u + 6) + 5 u
= 6 u + 6
= (6 x 11) + 6
= 66 + 6
= 72

Answer(s): 72