There are some red and brown beads in a box. If 5 red beads are removed from the box, the total number of beads left will be 8 times the number of red beads left. If 7 brown beads are removed from the box, the total number of beads left will be 5 times the number of red beads. How many beads are there in the box?

	Case 1		Case 2
	Red beads	Brown beads	Red beads	Brown beads
Before	1 u + 5	7 u	1 p	4 p + 7
Change	- 5			- 7
After	1 u	7 u	1 p	4 p

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

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

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

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

7 u = 4 p + 7
7 u - 7 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 20 = 4 p --- (3)

(2) = (3)
7 u - 7 = 4 u + 20
7 u - 4 u = 20 + 7
3 u = 27

1 u = 27 ÷ 3 = 9

Number of beads in the box
= (1 u + 5) + 7 u
= 8 u + 5
= (8 x 9) + 5
= 72 + 5
= 77

Answer(s): 77