There are some pink and purple marbles in a container. If 2 pink marbles are removed from the container, the total number of marbles left will be 7 times the number of pink marbles left. If 24 purple marbles are removed from the container, the total number of marbles left will be 4 times the number of pink marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Pink marbles |
Purple marbles |
Pink marbles |
Purple marbles |
Before |
1 u + 2 |
6 u |
1 p |
3 p + 24 |
Change |
- 2 |
|
|
- 24 |
After |
1 u |
6 u |
1 p |
3 p |
Number of purple marbles in the end for Case 1
= 7 u - 1 u
= 6 u
Number of pink marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of pink marbles at first is the same for Case 1 and Case 2.
The number of purple marbles at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
6 u = 3 p + 24
6 u - 24 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 6 =
3 p --- (3)
(2) = (3)
6 u - 24 = 3 u + 6
6 u - 3 u = 6 + 24
3 u = 30
1 u = 30 ÷ 3 = 10
Number of marbles in the container
= (1 u + 2) + 6 u
= 7 u + 2
= (7 x 10) + 2
= 70 + 2
= 72
Answer(s): 72