There are some purple and blue beads in a box. If 9 purple beads are removed from the box, the total number of beads left will be 9 times the number of purple beads left. If 4 blue beads are removed from the box, the total number of beads left will be 5 times the number of purple beads. How many beads are there in the box?

	Case 1		Case 2
	Purple beads	Blue beads	Purple beads	Blue beads
Before	1 u + 9	8 u	1 p	4 p + 4
Change	- 9			- 4
After	1 u	8 u	1 p	4 p

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

Number of purple beads in the end for Case 2
= 5 p - 1 p
= 4 p

The number of purple 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 + 9 = 1 p --- (1)

8 u = 4 p + 4
8 u - 4 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 36 = 4 p --- (3)

(2) = (3)
8 u - 4 = 4 u + 36
8 u - 4 u = 36 + 4
4 u = 40

1 u = 40 ÷ 4 = 10

Number of beads in the box
= (1 u + 9) + 8 u
= 9 u + 9
= (9 x 10) + 9
= 90 + 9
= 99

Answer(s): 99