There are some black and yellow beads in a box. If 7 black beads are removed from the box, the total number of beads left will be 8 times the number of black beads left. If 23 yellow beads are removed from the box, the total number of beads left will be 4 times the number of black beads. How many beads are there in the box?

	Case 1		Case 2
	Black beads	Yellow beads	Black beads	Yellow beads
Before	1 u + 7	7 u	1 p	3 p + 23
Change	- 7			- 23
After	1 u	7 u	1 p	3 p

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

Number of black beads in the end for Case 2
= 4 p - 1 p
= 3 p

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

1 u + 7 = 1 p --- (1)

7 u = 3 p + 23
7 u - 23 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 21 = 3 p --- (3)

(2) = (3)
7 u - 23 = 3 u + 21
7 u - 3 u = 21 + 23
4 u = 44

1 u = 44 ÷ 4 = 11

Number of beads in the box
= (1 u + 7) + 7 u
= 8 u + 7
= (8 x 11) + 7
= 88 + 7
= 95

Answer(s): 95