There are some white and red beads in a container. If 3 white beads are removed from the container, the total number of beads left will be 8 times the number of white beads left. If 4 red beads are removed from the container, the total number of beads left will be 3 times the number of white beads. How many beads are there in the container?

	Case 1		Case 2
	White beads	Red beads	White beads	Red beads
Before	1 u + 3	7 u	1 p	2 p + 4
Change	- 3			- 4
After	1 u	7 u	1 p	2 p

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

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

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

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

Make p the same.

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

(2) = (3)
7 u - 4 = 2 u + 6
7 u - 2 u = 6 + 4
5 u = 10

1 u = 10 ÷ 5 = 2

Number of beads in the container
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 2) + 3
= 16 + 3
= 19

Answer(s): 19