There are some pink and silver beads in a box. If 3 pink beads are removed from the box, the total number of beads left will be 9 times the number of pink beads left. If 36 silver beads are removed from the box, the total number of beads left will be 3 times the number of pink beads. How many beads are there in the box?

	Case 1		Case 2
	Pink beads	Silver beads	Pink beads	Silver beads
Before	1 u + 3	8 u	1 p	2 p + 36
Change	- 3			- 36
After	1 u	8 u	1 p	2 p

Number of silver beads in the end for Case 1
= 9 u - 1 u
= 8 u

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

The number of pink 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 + 3 = 1 p --- (1)

8 u = 2 p + 36
8 u - 36 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 6 = 2 p --- (3)

(2) = (3)
8 u - 36 = 2 u + 6
8 u - 2 u = 6 + 36
6 u = 42

1 u = 42 ÷ 6 = 7

Number of beads in the box
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 7) + 3
= 63 + 3
= 66

Answer(s): 66