There are some red and white beads in a container. If 3 red beads are removed from the container, the total number of beads left will be 5 times the number of red beads left. If 12 white beads are removed from the container, the total number of beads left will be 3 times the number of red beads. How many beads are there in the container?

	Case 1		Case 2
	Red beads	White beads	Red beads	White beads
Before	1 u + 3	4 u	1 p	2 p + 12
Change	- 3			- 12
After	1 u	4 u	1 p	2 p

Number of white beads in the end for Case 1
= 5 u - 1 u
= 4 u

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

The number of red beads at first is the same for Case 1 and Case 2.
The number of white beads at first is also the same for Case 1 and Case 2.

1 u + 3 = 1 p --- (1)

4 u = 2 p + 12
4 u - 12 = 2 p --- (2)

Make p the same.

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

(2) = (3)
4 u - 12 = 2 u + 6
4 u - 2 u = 6 + 12
2 u = 18

1 u = 18 ÷ 2 = 9

Number of beads in the container
= (1 u + 3) + 4 u
= 5 u + 3
= (5 x 9) + 3
= 45 + 3
= 48

Answer(s): 48