There are some purple and yellow beads in a box. If 3 purple beads are removed from the box, the total number of beads left will be 6 times the number of purple beads left. If 3 yellow beads are removed from the box, the total number of beads left will be 3 times the number of purple beads. How many beads are there in the box?

	Case 1		Case 2
	Purple beads	Yellow beads	Purple beads	Yellow beads
Before	1 u + 3	5 u	1 p	2 p + 3
Change	- 3			- 3
After	1 u	5 u	1 p	2 p

Number of yellow beads in the end for Case 1
= 6 u - 1 u
= 5 u

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

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

5 u = 2 p + 3
5 u - 3 = 2 p --- (2)

Make p the same.

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

(2) = (3)
5 u - 3 = 2 u + 6
5 u - 2 u = 6 + 3
3 u = 9

1 u = 9 ÷ 3 = 3

Number of beads in the box
= (1 u + 3) + 5 u
= 6 u + 3
= (6 x 3) + 3
= 18 + 3
= 21

Answer(s): 21