There are some blue and green beads in a box. If 2 blue beads are removed from the box, the total number of beads left will be 9 times the number of blue beads left. If 17 green beads are removed from the box, the total number of beads left will be 6 times the number of blue beads. How many beads are there in the box?

	Case 1		Case 2
	Blue beads	Green beads	Blue beads	Green beads
Before	1 u + 2	8 u	1 p	5 p + 17
Change	- 2			- 17
After	1 u	8 u	1 p	5 p

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

Number of blue beads in the end for Case 2
= 6 p - 1 p
= 5 p

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

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

8 u = 5 p + 17
8 u - 17 = 5 p --- (2)

Make p the same.

(1)_x5
5 u + 10 = 5 p --- (3)

(2) = (3)
8 u - 17 = 5 u + 10
8 u - 5 u = 10 + 17
3 u = 27

1 u = 27 ÷ 3 = 9

Number of beads in the box
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 9) + 2
= 81 + 2
= 83

Answer(s): 83