There are some black and gold beads in a container. If 2 black beads are removed from the container, the total number of beads left will be 7 times the number of black beads left. If 32 gold 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	Gold beads	Black beads	Gold beads
Before	1 u + 2	6 u	1 p	2 p + 32
Change	- 2			- 32
After	1 u	6 u	1 p	2 p

Number of gold beads in the end for Case 1
= 7 u - 1 u
= 6 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 gold beads at first is also the same for Case 1 and Case 2.

1 u + 2 = 1 p --- (1)

6 u = 2 p + 32
6 u - 32 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
6 u - 32 = 2 u + 4
6 u - 2 u = 4 + 32
4 u = 36

1 u = 36 ÷ 4 = 9

Number of beads in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 9) + 2
= 63 + 2
= 65

Answer(s): 65