There are some grey and purple marbles in a container. If 5 grey marbles are removed from the container, the total number of marbles left will be 9 times the number of grey marbles left. If 5 purple marbles are removed from the container, the total number of marbles left will be 4 times the number of grey marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Grey marbles |
Purple marbles |
Grey marbles |
Purple marbles |
Before |
1 u + 5 |
8 u |
1 p |
3 p + 5 |
Change |
- 5 |
|
|
- 5 |
After |
1 u |
8 u |
1 p |
3 p |
Number of purple marbles in the end for Case 1
= 9 u - 1 u
= 8 u
Number of grey marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of grey 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 + 5 = 1 p --- (1)
8 u = 3 p + 5
8 u - 5 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 15 =
3 p --- (3)
(2) = (3)
8 u - 5 = 3 u + 15
8 u - 3 u = 15 + 5
5 u = 20
1 u = 20 ÷ 5 = 4
Number of marbles in the container
= (1 u + 5) + 8 u
= 9 u + 5
= (9 x 4) + 5
= 36 + 5
= 41
Answer(s): 41