There are some gold and black beads in a box. If 2 gold beads are removed from the box, the total number of beads left will be 6 times the number of gold beads left. If 23 black beads are removed from the box, the total number of beads left will be 3 times the number of gold beads. How many beads are there in the box?

	Case 1		Case 2
	Gold beads	Black beads	Gold beads	Black beads
Before	1 u + 2	5 u	1 p	2 p + 23
Change	- 2			- 23
After	1 u	5 u	1 p	2 p

Number of black beads in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

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

5 u = 2 p + 23
5 u - 23 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 23 = 2 u + 4
5 u - 2 u = 4 + 23
3 u = 27

1 u = 27 ÷ 3 = 9

Number of beads in the box
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 9) + 2
= 54 + 2
= 56

Answer(s): 56