There are some brown and pink beads in a container. If 7 brown beads are removed from the container, the total number of beads left will be 9 times the number of brown beads left. If 4 pink 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 |
Pink beads |
Brown beads |
Pink beads |
Before |
1 u + 7 |
8 u |
1 p |
2 p + 4 |
Change |
- 7 |
|
|
- 4 |
After |
1 u |
8 u |
1 p |
2 p |
Number of pink beads in the end for Case 1
= 9 u - 1 u
= 8 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 pink beads at first is also the same for Case 1 and Case 2.
1 u + 7 = 1 p --- (1)
8 u = 2 p + 4
8 u - 4 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 14 =
2 p --- (3)
(2) = (3)
8 u - 4 = 2 u + 14
8 u - 2 u = 14 + 4
6 u = 18
1 u = 18 ÷ 6 = 3
Number of beads in the container
= (1 u + 7) + 8 u
= 9 u + 7
= (9 x 3) + 7
= 27 + 7
= 34
Answer(s): 34