There are some green and silver beads in a container. If 3 green beads are removed from the container, the total number of beads left will be 7 times the number of green beads left. If 6 silver beads are removed from the container, the total number of beads left will be 3 times the number of green beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Green beads |
Silver beads |
Green beads |
Silver beads |
Before |
1 u + 3 |
6 u |
1 p |
2 p + 6 |
Change |
- 3 |
|
|
- 6 |
After |
1 u |
6 u |
1 p |
2 p |
Number of silver beads in the end for Case 1
= 7 u - 1 u
= 6 u
Number of green beads in the end for Case 2
= 3 p - 1 p
= 2 p
The number of green 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 + 3 = 1 p --- (1)
6 u = 2 p + 6
6 u - 6 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 6 =
2 p --- (3)
(2) = (3)
6 u - 6 = 2 u + 6
6 u - 2 u = 6 + 6
4 u = 12
1 u = 12 ÷ 4 = 3
Number of beads in the container
= (1 u + 3) + 6 u
= 7 u + 3
= (7 x 3) + 3
= 21 + 3
= 24
Answer(s): 24