There are some brown and silver beads in a box. If 5 brown beads are removed from the box, the total number of beads left will be 7 times the number of brown beads left. If 18 silver beads are removed from the box, the total number of beads left will be 3 times the number of brown beads. How many beads are there in the box?

	Case 1		Case 2
	Brown beads	Silver beads	Brown beads	Silver beads
Before	1 u + 5	6 u	1 p	2 p + 18
Change	- 5			- 18
After	1 u	6 u	1 p	2 p

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

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

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

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

6 u = 2 p + 18
6 u - 18 = 2 p --- (2)

Make p the same.

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

(2) = (3)
6 u - 18 = 2 u + 10
6 u - 2 u = 10 + 18
4 u = 28

1 u = 28 ÷ 4 = 7

Number of beads in the box
= (1 u + 5) + 6 u
= 7 u + 5
= (7 x 7) + 5
= 49 + 5
= 54

Answer(s): 54