There are some brown and silver beads in a container. If 5 brown beads are removed from the container, the total number of beads left will be 6 times the number of brown beads left. If 8 silver beads are removed from the container, the total number of beads left will be 3 times the number of brown beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Brown beads |
Silver beads |
Brown beads |
Silver beads |
Before |
1 u + 5 |
5 u |
1 p |
2 p + 8 |
Change |
- 5 |
|
|
- 8 |
After |
1 u |
5 u |
1 p |
2 p |
Number of silver beads in the end for Case 1
= 6 u - 1 u
= 5 u
Number of brown beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of brown beads at first is the same for Case 1 and Case 2.
The number of silver beads at first is also the same for Case 1 and Case 2.
1 u + 5 = 1 p --- (1)
5 u = 2 p + 8
5 u - 8 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 10 =
2 p --- (3)
(2) = (3)
5 u - 8 = 2 u + 10
5 u - 2 u = 10 + 8
3 u = 18
1 u = 18 ÷ 3 = 6
Number of beads in the container
= (1 u + 5) + 5 u
= 6 u + 5
= (6 x 6) + 5
= 36 + 5
= 41
Answer(s): 41