There are some green and silver marbles in a container. If 2 green marbles are removed from the container, the total number of marbles left will be 6 times the number of green marbles left. If 23 silver marbles are removed from the container, the total number of marbles left will be 3 times the number of green marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Green marbles |
Silver marbles |
Green marbles |
Silver marbles |
Before |
1 u + 2 |
5 u |
1 p |
2 p + 23 |
Change |
- 2 |
|
|
- 23 |
After |
1 u |
5 u |
1 p |
2 p |
Number of silver marbles in the end for Case 1
= 6 u - 1 u
= 5 u
Number of green marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of green marbles at first is the same for Case 1 and Case 2.
The number of silver marbles at first is also the same for Case 1 and Case 2.
1 u + 2 = 1 p --- (1)
5 u = 2 p + 23
5 u - 23 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 4 =
2 p --- (3)
(2) = (3)
5 u - 23 = 2 u + 4
5 u - 2 u = 4 + 23
3 u = 27
1 u = 27 ÷ 3 = 9
Number of marbles in the container
= (1 u + 2) + 5 u
= 6 u + 2
= (6 x 9) + 2
= 54 + 2
= 56
Answer(s): 56