There are some yellow and grey marbles in a container. If 6 yellow marbles are removed from the container, the total number of marbles left will be 5 times the number of yellow marbles left. If 2 grey marbles are removed from the container, the total number of marbles left will be 3 times the number of yellow marbles. How many marbles are there in the container?
|
Case 1 |
Case 2 |
|
Yellow marbles |
Grey marbles |
Yellow marbles |
Grey marbles |
Before |
1 u + 6 |
4 u |
1 p |
2 p + 2 |
Change |
- 6 |
|
|
- 2 |
After |
1 u |
4 u |
1 p |
2 p |
Number of grey marbles in the end for Case 1
= 5 u - 1 u
= 4 u
Number of yellow marbles in the end for Case 2
= 3 p - 1 p
= 2 p
The number of yellow marbles at first is the same for Case 1 and Case 2.
The number of grey marbles at first is also the same for Case 1 and Case 2.
1 u + 6 = 1 p --- (1)
4 u = 2 p + 2
4 u - 2 =
2 p --- (2)
Make p the same.
(1)
x2 2 u + 12 =
2 p --- (3)
(2) = (3)
4 u - 2 = 2 u + 12
4 u - 2 u = 12 + 2
2 u = 14
1 u = 14 ÷ 2 = 7
Number of marbles in the container
= (1 u + 6) + 4 u
= 5 u + 6
= (5 x 7) + 6
= 35 + 6
= 41
Answer(s): 41