There are some green and silver beads in a box. If 10 green beads are removed from the box, the total number of beads left will be 9 times the number of green beads left. If 46 silver beads are removed from the box, the total number of beads left will be 3 times the number of green beads. How many beads are there in the box?

	Case 1		Case 2
	Green beads	Silver beads	Green beads	Silver beads
Before	1 u + 10	8 u	1 p	2 p + 46
Change	- 10			- 46
After	1 u	8 u	1 p	2 p

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

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

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

1 u + 10 = 1 p --- (1)

8 u = 2 p + 46
8 u - 46 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 20 = 2 p --- (3)

(2) = (3)
8 u - 46 = 2 u + 20
8 u - 2 u = 20 + 46
6 u = 66

1 u = 66 ÷ 6 = 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