There are some yellow and green beads in a container. If 2 yellow beads are removed from the container, the total number of beads left will be 7 times the number of yellow beads left. If 36 green 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	Green beads	Yellow beads	Green beads
Before	1 u + 2	6 u	1 p	2 p + 36
Change	- 2			- 36
After	1 u	6 u	1 p	2 p

Number of green 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 green beads at first is also the same for Case 1 and Case 2.

1 u + 2 = 1 p --- (1)

6 u = 2 p + 36
6 u - 36 = 2 p --- (2)

Make p the same.

(1)_x2
2 u + 4 = 2 p --- (3)

(2) = (3)
6 u - 36 = 2 u + 4
6 u - 2 u = 4 + 36
4 u = 40

1 u = 40 ÷ 4 = 10

Number of beads in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 10) + 2
= 70 + 2
= 72

Answer(s): 72