There are some purple and pink beads in a container. If 3 purple beads are removed from the container, the total number of beads left will be 7 times the number of purple beads left. If 18 pink beads are removed from the container, the total number of beads left will be 4 times the number of purple beads. How many beads are there in the container?

	Case 1		Case 2
	Purple beads	Pink beads	Purple beads	Pink beads
Before	1 u + 3	6 u	1 p	3 p + 18
Change	- 3			- 18
After	1 u	6 u	1 p	3 p

Number of pink beads in the end for Case 1
= 7 u - 1 u
= 6 u

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

The number of purple 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)

6 u = 3 p + 18
6 u - 18 = 3 p --- (2)

Make p the same.

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

(2) = (3)
6 u - 18 = 3 u + 9
6 u - 3 u = 9 + 18
3 u = 27

1 u = 27 ÷ 3 = 9

Number of beads in the container
= (1 u + 3) + 6 u
= 7 u + 3
= (7 x 9) + 3
= 63 + 3
= 66

Answer(s): 66