There are some green and pink beads in a container. If 4 green beads are removed from the container, the total number of beads left will be 7 times the number of green beads left. If 3 pink beads are removed from the container, the total number of beads left will be 4 times the number of green beads. How many beads are there in the container?
|
Case 1 |
Case 2 |
|
Green beads |
Pink beads |
Green beads |
Pink beads |
Before |
1 u + 4 |
6 u |
1 p |
3 p + 3 |
Change |
- 4 |
|
|
- 3 |
After |
1 u |
6 u |
1 p |
3 p |
Number of pink beads in the end for Case 1
= 7 u - 1 u
= 6 u
Number of green beads in the end for Case 2
= 4 p - 1 p
= 3 p
The number of green 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 + 4 = 1 p --- (1)
6 u = 3 p + 3
6 u - 3 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 12 =
3 p --- (3)
(2) = (3)
6 u - 3 = 3 u + 12
6 u - 3 u = 12 + 3
3 u = 15
1 u = 15 ÷ 3 = 5
Number of beads in the container
= (1 u + 4) + 6 u
= 7 u + 4
= (7 x 5) + 4
= 35 + 4
= 39
Answer(s): 39