There are some brown and red beads in a container. If 3 brown beads are removed from the container, the total number of beads left will be 9 times the number of brown beads left. If 41 red beads are removed from the container, the total number of beads left will be 4 times the number of brown beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Brown beads |
Red beads |
Brown beads |
Red beads |
Before |
1 u + 3 |
8 u |
1 p |
3 p + 41 |
Change |
- 3 |
|
|
- 41 |
After |
1 u |
8 u |
1 p |
3 p |
Number of red beads in the end for Case 1
= 9 u - 1 u
= 8 u
Number of brown beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of brown beads at first is the same for Case 1 and Case 2.
The number of red beads at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
8 u = 3 p + 41
8 u - 41 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 9 =
3 p --- (3)
(2) = (3)
8 u - 41 = 3 u + 9
8 u - 3 u = 9 + 41
5 u = 50
1 u = 50 ÷ 5 = 10
Number of beads in the container
= (1 u + 3) + 8 u
= 9 u + 3
= (9 x 10) + 3
= 90 + 3
= 93
Answer(s): 93