There are some black and silver beads in a container. If 8 black beads are removed from the container, the total number of beads left will be 9 times the number of black beads left. If 56 silver beads are removed from the container, the total number of beads left will be 3 times the number of black beads. How many beads are there in the container?

	Case 1		Case 2
	Black beads	Silver beads	Black beads	Silver beads
Before	1 u + 8	8 u	1 p	2 p + 56
Change	- 8			- 56
After	1 u	8 u	1 p	2 p

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

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

The number of black 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 + 8 = 1 p --- (1)

8 u = 2 p + 56
8 u - 56 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
8 u - 56 = 2 u + 16
8 u - 2 u = 16 + 56
6 u = 72

1 u = 72 ÷ 6 = 12

Number of beads in the container
= (1 u + 8) + 8 u
= 9 u + 8
= (9 x 12) + 8
= 108 + 8
= 116

Answer(s): 116