There are some gold and white beads in a container. If 7 gold beads are removed from the container, the total number of beads left will be 8 times the number of gold beads left. If 11 white beads are removed from the container, the total number of beads left will be 4 times the number of gold beads. How many beads are there in the container?

	Case 1		Case 2
	Gold beads	White beads	Gold beads	White beads
Before	1 u + 7	7 u	1 p	3 p + 11
Change	- 7			- 11
After	1 u	7 u	1 p	3 p

Number of white beads in the end for Case 1
= 8 u - 1 u
= 7 u

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

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

1 u + 7 = 1 p --- (1)

7 u = 3 p + 11
7 u - 11 = 3 p --- (2)

Make p the same.

(1)_x3
3 u + 21 = 3 p --- (3)

(2) = (3)
7 u - 11 = 3 u + 21
7 u - 3 u = 21 + 11
4 u = 32

1 u = 32 ÷ 4 = 8

Number of beads in the container
= (1 u + 7) + 7 u
= 8 u + 7
= (8 x 8) + 7
= 64 + 7
= 71

Answer(s): 71