There are some blue and white beads in a box. If 6 blue beads are removed from the box, the total number of beads left will be 8 times the number of blue beads left. If 14 white 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	White beads	Blue beads	White beads
Before	1 u + 6	7 u	1 p	3 p + 14
Change	- 6			- 14
After	1 u	7 u	1 p	3 p

Number of white beads in the end for Case 1
= 8 u - 1 u
= 7 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 white beads at first is also the same for Case 1 and Case 2.

1 u + 6 = 1 p --- (1)

7 u = 3 p + 14
7 u - 14 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 18 = 3 p --- (3)

(2) = (3)
7 u - 14 = 3 u + 18
7 u - 3 u = 18 + 14
4 u = 32

1 u = 32 ÷ 4 = 8

Number of beads in the box
= (1 u + 6) + 7 u
= 8 u + 6
= (8 x 8) + 6
= 64 + 6
= 70

Answer(s): 70