There are some black and gold beads in a container. If 6 black beads are removed from the container, the total number of beads left will be 9 times the number of black beads left. If 32 gold beads are removed from the container, the total number of beads left will be 4 times the number of black beads. How many beads are there in the container?

	Case 1		Case 2
	Black beads	Gold beads	Black beads	Gold beads
Before	1 u + 6	8 u	1 p	3 p + 32
Change	- 6			- 32
After	1 u	8 u	1 p	3 p

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

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

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

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

8 u = 3 p + 32
8 u - 32 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 18 = 3 p --- (3)

(2) = (3)
8 u - 32 = 3 u + 18
8 u - 3 u = 18 + 32
5 u = 50

1 u = 50 ÷ 5 = 10

Number of beads in the container
= (1 u + 6) + 8 u
= 9 u + 6
= (9 x 10) + 6
= 90 + 6
= 96

Answer(s): 96