There are some brown and purple beads in a container. If 4 brown beads are removed from the container, the total number of beads left will be 8 times the number of brown beads left. If 20 purple 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	Purple beads	Brown beads	Purple beads
Before	1 u + 4	7 u	1 p	4 p + 20
Change	- 4			- 20
After	1 u	7 u	1 p	4 p

Number of purple beads in the end for Case 1
= 8 u - 1 u
= 7 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 purple beads at first is also the same for Case 1 and Case 2.

1 u + 4 = 1 p --- (1)

7 u = 4 p + 20
7 u - 20 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 16 = 4 p --- (3)

(2) = (3)
7 u - 20 = 4 u + 16
7 u - 4 u = 16 + 20
3 u = 36

1 u = 36 ÷ 3 = 12

Number of beads in the container
= (1 u + 4) + 7 u
= 8 u + 4
= (8 x 12) + 4
= 96 + 4
= 100

Answer(s): 100