There are some red and silver marbles in a container. If 2 red marbles are removed from the container, the total number of marbles left will be 8 times the number of red marbles left. If 16 silver marbles are removed from the container, the total number of marbles left will be 5 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 + 2 |
7 u |
1 p |
4 p + 16 |
Change |
- 2 |
|
|
- 16 |
After |
1 u |
7 u |
1 p |
4 p |
Number of silver marbles in the end for Case 1
= 8 u - 1 u
= 7 u
Number of red marbles in the end for Case 2
= 5 p - 1 p
= 4 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 + 2 = 1 p --- (1)
7 u = 4 p + 16
7 u - 16 =
4 p --- (2)
Make p the same.
(1)
x4 4 u + 8 =
4 p --- (3)
(2) = (3)
7 u - 16 = 4 u + 8
7 u - 4 u = 8 + 16
3 u = 24
1 u = 24 ÷ 3 = 8
Number of marbles in the container
= (1 u + 2) + 7 u
= 8 u + 2
= (8 x 8) + 2
= 64 + 2
= 66
Answer(s): 66