There are some blue and yellow beads in a container. If 2 blue beads are removed from the container, the total number of beads left will be 9 times the number of blue beads left. If 8 yellow beads are removed from the container, the total number of beads left will be 5 times the number of blue beads. How many beads are there in the container?

	Case 1		Case 2
	Blue beads	Yellow beads	Blue beads	Yellow beads
Before	1 u + 2	8 u	1 p	4 p + 8
Change	- 2			- 8
After	1 u	8 u	1 p	4 p

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

Number of blue beads in the end for Case 2
= 5 p - 1 p
= 4 p

The number of blue 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 + 2 = 1 p --- (1)

8 u = 4 p + 8
8 u - 8 = 4 p --- (2)

Make p the same.

(1)_x4
4 u + 8 = 4 p --- (3)

(2) = (3)
8 u - 8 = 4 u + 8
8 u - 4 u = 8 + 8
4 u = 16

1 u = 16 ÷ 4 = 4

Number of beads in the container
= (1 u + 2) + 8 u
= 9 u + 2
= (9 x 4) + 2
= 36 + 2
= 38

Answer(s): 38