There are some yellow and black beads in a container. If 4 yellow beads are removed from the container, the total number of beads left will be 7 times the number of yellow beads left. If 40 black beads are removed from the container, the total number of beads left will be 3 times the number of yellow beads. How many beads are there in the container?

	Case 1		Case 2
	Yellow beads	Black beads	Yellow beads	Black beads
Before	1 u + 4	6 u	1 p	2 p + 40
Change	- 4			- 40
After	1 u	6 u	1 p	2 p

Number of black beads in the end for Case 1
= 7 u - 1 u
= 6 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 black beads at first is also the same for Case 1 and Case 2.

1 u + 4 = 1 p --- (1)

6 u = 2 p + 40
6 u - 40 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 8 = 2 p --- (3)

(2) = (3)
6 u - 40 = 2 u + 8
6 u - 2 u = 8 + 40
4 u = 48

1 u = 48 ÷ 4 = 12

Number of beads in the container
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 12) + 4
= 84 + 4
= 88

Answer(s): 88