There are some gold and blue beads in a box. If 2 gold beads are removed from the box, the total number of beads left will be 4 times the number of gold beads left. If 3 blue 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	Blue beads	Gold beads	Blue beads
Before	1 u + 2	3 u	1 p	2 p + 3
Change	- 2			- 3
After	1 u	3 u	1 p	2 p

Number of blue beads in the end for Case 1
= 4 u - 1 u
= 3 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 blue beads at first is also the same for Case 1 and Case 2.

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

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

Make p the same.

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

(2) = (3)
3 u - 3 = 2 u + 4
3 u - 2 u = 4 + 3
1 u = 7

1 u = 7 ÷ 1 = 7

Number of beads in the box
= (1 u + 2) + 3 u
= 4 u + 2
= (4 x 7) + 2
= 28 + 2
= 30

Answer(s): 30