There are some yellow and silver beads in a box. If 4 yellow beads are removed from the box, the total number of beads left will be 8 times the number of yellow beads left. If 47 silver beads are removed from the box, the total number of beads left will be 3 times the number of yellow beads. How many beads are there in the box?

	Case 1		Case 2
	Yellow beads	Silver beads	Yellow beads	Silver beads
Before	1 u + 4	7 u	1 p	2 p + 47
Change	- 4			- 47
After	1 u	7 u	1 p	2 p

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

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

The number of yellow 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 + 4 = 1 p --- (1)

7 u = 2 p + 47
7 u - 47 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
7 u - 47 = 2 u + 8
7 u - 2 u = 8 + 47
5 u = 55

1 u = 55 ÷ 5 = 11

Number of beads in the box
= (1 u + 4) + 7 u
= 8 u + 4
= (8 x 11) + 4
= 88 + 4
= 92

Answer(s): 92