There are some red and silver marbles in a container. If 4 red marbles are removed from the container, the total number of marbles left will be 9 times the number of red marbles left. If 3 silver marbles are removed from the container, the total number of marbles left will be 4 times the number of red marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Red marbles |
Silver marbles |
Red marbles |
Silver marbles |
Before |
1 u + 4 |
8 u |
1 p |
3 p + 3 |
Change |
- 4 |
|
|
- 3 |
After |
1 u |
8 u |
1 p |
3 p |
Number of silver marbles in the end for Case 1
= 9 u - 1 u
= 8 u
Number of red marbles in the end for Case 2
= 4 p - 1 p
= 3 p
The number of red 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 + 4 = 1 p --- (1)
8 u = 3 p + 3
8 u - 3 =
3 p --- (2)
Make p the same.
(1)
x3 3 u + 12 =
3 p --- (3)
(2) = (3)
8 u - 3 = 3 u + 12
8 u - 3 u = 12 + 3
5 u = 15
1 u = 15 ÷ 5 = 3
Number of marbles in the container
= (1 u + 4) + 8 u
= 9 u + 4
= (9 x 3) + 4
= 27 + 4
= 31
Answer(s): 31