There are some yellow and pink beads in a box. If 3 yellow beads are removed from the box, the total number of beads left will be 5 times the number of yellow beads left. If 2 pink beads are removed from the box, the total number of beads left will be 3 times the number of yellow beads. How many beads are there in the box?

	Case 1		Case 2
	Yellow beads	Pink beads	Yellow beads	Pink beads
Before	1 u + 3	4 u	1 p	2 p + 2
Change	- 3			- 2
After	1 u	4 u	1 p	2 p

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

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

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

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

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

Make p the same.

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

(2) = (3)
4 u - 2 = 2 u + 6
4 u - 2 u = 6 + 2
2 u = 8

1 u = 8 ÷ 2 = 4

Number of beads in the box
= (1 u + 3) + 4 u
= 5 u + 3
= (5 x 4) + 3
= 20 + 3
= 23

Answer(s): 23