There are some pink and red beads in a box. If 7 pink beads are removed from the box, the total number of beads left will be 8 times the number of pink beads left. If 27 red beads are removed from the box, the total number of beads left will be 4 times the number of pink beads. How many beads are there in the box?

	Case 1		Case 2
	Pink beads	Red beads	Pink beads	Red beads
Before	1 u + 7	7 u	1 p	3 p + 27
Change	- 7			- 27
After	1 u	7 u	1 p	3 p

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

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

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

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

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

Make p the same.

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

(2) = (3)
7 u - 27 = 3 u + 21
7 u - 3 u = 21 + 27
4 u = 48

1 u = 48 ÷ 4 = 12

Number of beads in the box
= (1 u + 7) + 7 u
= 8 u + 7
= (8 x 12) + 7
= 96 + 7
= 103

Answer(s): 103