There are some black and blue beads in a box. If 3 black beads are removed from the box, the total number of beads left will be 7 times the number of black beads left. If 42 blue beads are removed from the box, the total number of beads left will be 3 times the number of black beads. How many beads are there in the box?

	Case 1		Case 2
	Black beads	Blue beads	Black beads	Blue beads
Before	1 u + 3	6 u	1 p	2 p + 42
Change	- 3			- 42
After	1 u	6 u	1 p	2 p

Number of blue beads in the end for Case 1
= 7 u - 1 u
= 6 u

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

The number of black 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 + 3 = 1 p --- (1)

6 u = 2 p + 42
6 u - 42 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
6 u - 42 = 2 u + 6
6 u - 2 u = 6 + 42
4 u = 48

1 u = 48 ÷ 4 = 12

Number of beads in the box
= (1 u + 3) + 6 u
= 7 u + 3
= (7 x 12) + 3
= 84 + 3
= 87

Answer(s): 87