There are some green and silver beads in a container. If 5 green beads are removed from the container, the total number of beads left will be 9 times the number of green beads left. If 20 silver beads are removed from the container, the total number of beads left will be 4 times the number of green beads. How many beads are there in the container?

	Case 1		Case 2
	Green beads	Silver beads	Green beads	Silver beads
Before	1 u + 5	8 u	1 p	3 p + 20
Change	- 5			- 20
After	1 u	8 u	1 p	3 p

Number of silver beads in the end for Case 1
= 9 u - 1 u
= 8 u

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

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

1 u + 5 = 1 p --- (1)

8 u = 3 p + 20
8 u - 20 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 15 = 3 p --- (3)

(2) = (3)
8 u - 20 = 3 u + 15
8 u - 3 u = 15 + 20
5 u = 35

1 u = 35 ÷ 5 = 7

Number of beads in the container
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 7) + 5
= 63 + 5
= 68

Answer(s): 68