There are some pink and black beads in a container. If 3 pink beads are removed from the container, the total number of beads left will be 8 times the number of pink beads left. If 3 black beads are removed from the container, the total number of beads left will be 4 times the number of pink beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Pink beads |
Black beads |
Pink beads |
Black beads |
Before |
1 u + 3 |
7 u |
1 p |
3 p + 3 |
Change |
- 3 |
|
|
- 3 |
After |
1 u |
7 u |
1 p |
3 p |
Number of black beads in the end for Case 1
= 8 u - 1 u
= 7 u
Number of pink beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of pink beads at first is the same for Case 1 and Case 2.
The number of black beads at first is also the same for Case 1 and Case 2.
1 u + 3 = 1 p --- (1)
7 u = 3 p + 3
7 u - 3 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 9 =
3 p --- (3)
(2) = (3)
7 u - 3 = 3 u + 9
7 u - 3 u = 9 + 3
4 u = 12
1 u = 12 ÷ 4 = 3
Number of beads in the container
= (1 u + 3) + 7 u
= 8 u + 3
= (8 x 3) + 3
= 24 + 3
= 27
Answer(s): 27