There are some blue and green beads in a box. If 3 blue beads are removed from the box, the total number of beads left will be 8 times the number of blue beads left. If 27 green 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	Green beads	Blue beads	Green beads
Before	1 u + 3	7 u	1 p	3 p + 27
Change	- 3			- 27
After	1 u	7 u	1 p	3 p

Number of green 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 green beads at first is also the same for Case 1 and Case 2.

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

7 u = 3 p + 27
7 u - 27 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 9 = 3 p --- (3)

(2) = (3)
7 u - 27 = 3 u + 9
7 u - 3 u = 9 + 27
4 u = 36

1 u = 36 ÷ 4 = 9

Number of beads in the box
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 9) + 3
= 72 + 3
= 75

Answer(s): 75