There are some black and brown beads in a container. If 8 black beads are removed from the container, the total number of beads left will be 5 times the number of black beads left. If 2 brown beads are removed from the container, the total number of beads left will be 3 times the number of black beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Black beads |
Brown beads |
Black beads |
Brown beads |
Before |
1 u + 8 |
4 u |
1 p |
2 p + 2 |
Change |
- 8 |
|
|
- 2 |
After |
1 u |
4 u |
1 p |
2 p |
Number of brown beads in the end for Case 1
= 5 u - 1 u
= 4 u
Number of black beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of black beads at first is the same for Case 1 and Case 2.
The number of brown beads at first is also the same for Case 1 and Case 2.
1 u + 8 = 1 p --- (1)
4 u = 2 p + 2
4 u - 2 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 16 =
2 p --- (3)
(2) = (3)
4 u - 2 = 2 u + 16
4 u - 2 u = 16 + 2
2 u = 18
1 u = 18 ÷ 2 = 9
Number of beads in the container
= (1 u + 8) + 4 u
= 5 u + 8
= (5 x 9) + 8
= 45 + 8
= 53
Answer(s): 53