There are some blue and gold beads in a box. If 10 blue beads are removed from the box, the total number of beads left will be 9 times the number of blue beads left. If 25 gold beads are removed from the box, the total number of beads left will be 4 times the number of blue beads. How many beads are there in the box?

	Case 1		Case 2
	Blue beads	Gold beads	Blue beads	Gold beads
Before	1 u + 10	8 u	1 p	3 p + 25
Change	- 10			- 25
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 blue beads in the end for Case 2
= 4 p - 1 p
= 3 p

The number of blue 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 + 10 = 1 p --- (1)

8 u = 3 p + 25
8 u - 25 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 30 = 3 p --- (3)

(2) = (3)
8 u - 25 = 3 u + 30
8 u - 3 u = 30 + 25
5 u = 55

1 u = 55 ÷ 5 = 11

Number of beads in the box
= (1 u + 10) + 8 u
= 9 u + 10
= (9 x 11) + 10
= 99 + 10
= 109

Answer(s): 109