There are some gold and red beads in a container. If 3 gold beads are removed from the container, the total number of beads left will be 9 times the number of gold beads left. If 21 red beads are removed from the container, the total number of beads left will be 4 times the number of gold beads. How many beads are there in the container?

	Case 1		Case 2
	Gold beads	Red beads	Gold beads	Red beads
Before	1 u + 3	8 u	1 p	3 p + 21
Change	- 3			- 21
After	1 u	8 u	1 p	3 p

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

Number of gold beads in the end for Case 2
= 4 p - 1 p
= 3 p

The number of gold 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)

8 u = 3 p + 21
8 u - 21 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 9 = 3 p --- (3)

(2) = (3)
8 u - 21 = 3 u + 9
8 u - 3 u = 9 + 21
5 u = 30

1 u = 30 ÷ 5 = 6

Number of beads in the container
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 6) + 3
= 54 + 3
= 57

Answer(s): 57