There are some white and red beads in a container. If 4 white beads are removed from the container, the total number of beads left will be 7 times the number of white beads left. If 20 red beads are removed from the container, the total number of beads left will be 3 times the number of white beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
White beads |
Red beads |
White beads |
Red beads |
Before |
1 u + 4 |
6 u |
1 p |
2 p + 20 |
Change |
- 4 |
|
|
- 20 |
After |
1 u |
6 u |
1 p |
2 p |
Number of red beads in the end for Case 1
= 7 u - 1 u
= 6 u
Number of white beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of white 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 + 4 = 1 p --- (1)
6 u = 2 p + 20
6 u - 20 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 8 =
2 p --- (3)
(2) = (3)
6 u - 20 = 2 u + 8
6 u - 2 u = 8 + 20
4 u = 28
1 u = 28 ÷ 4 = 7
Number of beads in the container
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 7) + 4
= 49 + 4
= 53
Answer(s): 53