There are some pink and green beads in a container. If 9 pink beads are removed from the container, the total number of beads left will be 8 times the number of pink beads left. If 37 green 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	Green beads	Pink beads	Green beads
Before	1 u + 9	7 u	1 p	2 p + 37
Change	- 9			- 37
After	1 u	7 u	1 p	2 p

Number of green beads in the end for Case 1
= 8 u - 1 u
= 7 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 green beads at first is also the same for Case 1 and Case 2.

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

7 u = 2 p + 37
7 u - 37 = 2 p --- (2)

Make p the same.

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

(2) = (3)
7 u - 37 = 2 u + 18
7 u - 2 u = 18 + 37
5 u = 55

1 u = 55 ÷ 5 = 11

Number of beads in the container
= (1 u + 9) + 7 u
= 8 u + 9
= (8 x 11) + 9
= 88 + 9
= 97

Answer(s): 97