There are some pink and grey beads in a container. If 9 pink beads are removed from the container, the total number of beads left will be 9 times the number of pink beads left. If 48 grey beads are removed from the container, the total number of beads left will be 3 times the number of pink beads. How many beads are there in the container?

	Case 1		Case 2
	Pink beads	Grey beads	Pink beads	Grey beads
Before	1 u + 9	8 u	1 p	2 p + 48
Change	- 9			- 48
After	1 u	8 u	1 p	2 p

Number of grey 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 grey beads at first is also the same for Case 1 and Case 2.

1 u + 9 = 1 p --- (1)

8 u = 2 p + 48
8 u - 48 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 18 = 2 p --- (3)

(2) = (3)
8 u - 48 = 2 u + 18
8 u - 2 u = 18 + 48
6 u = 66

1 u = 66 ÷ 6 = 11

Number of beads in the container
= (1 u + 9) + 8 u
= 9 u + 9
= (9 x 11) + 9
= 99 + 9
= 108

Answer(s): 108