There are some purple and red beads in a container. If 8 purple beads are removed from the container, the total number of beads left will be 8 times the number of purple beads left. If 39 red beads are removed from the container, the total number of beads left will be 3 times the number of purple beads. How many beads are there in the container?

	Case 1		Case 2
	Purple beads	Red beads	Purple beads	Red beads
Before	1 u + 8	7 u	1 p	2 p + 39
Change	- 8			- 39
After	1 u	7 u	1 p	2 p

Number of red beads in the end for Case 1
= 8 u - 1 u
= 7 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 red beads at first is also the same for Case 1 and Case 2.

1 u + 8 = 1 p --- (1)

7 u = 2 p + 39
7 u - 39 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 16 = 2 p --- (3)

(2) = (3)
7 u - 39 = 2 u + 16
7 u - 2 u = 16 + 39
5 u = 55

1 u = 55 ÷ 5 = 11

Number of beads in the container
= (1 u + 8) + 7 u
= 8 u + 8
= (8 x 11) + 8
= 88 + 8
= 96

Answer(s): 96