There are some white and red beads in a box. If 5 white beads are removed from the box, the total number of beads left will be 8 times the number of white beads left. If 45 red beads are removed from the box, the total number of beads left will be 3 times the number of white beads. How many beads are there in the box?

	Case 1		Case 2
	White beads	Red beads	White beads	Red beads
Before	1 u + 5	7 u	1 p	2 p + 45
Change	- 5			- 45
After	1 u	7 u	1 p	2 p

Number of red beads in the end for Case 1
= 8 u - 1 u
= 7 u

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

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

1 u + 5 = 1 p --- (1)

7 u = 2 p + 45
7 u - 45 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 10 = 2 p --- (3)

(2) = (3)
7 u - 45 = 2 u + 10
7 u - 2 u = 10 + 45
5 u = 55

1 u = 55 ÷ 5 = 11

Number of beads in the box
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 11) + 5
= 88 + 5
= 93

Answer(s): 93