There are some black and white beads in a container. If 5 black beads are removed from the container, the total number of beads left will be 9 times the number of black beads left. If 8 white beads are removed from the container, the total number of beads left will be 5 times the number of black beads. How many beads are there in the container?

	Case 1		Case 2
	Black beads	White beads	Black beads	White beads
Before	1 u + 5	8 u	1 p	4 p + 8
Change	- 5			- 8
After	1 u	8 u	1 p	4 p

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

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

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

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

8 u = 4 p + 8
8 u - 8 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 20 = 4 p --- (3)

(2) = (3)
8 u - 8 = 4 u + 20
8 u - 4 u = 20 + 8
4 u = 28

1 u = 28 ÷ 4 = 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