Container E contains 14 grey marbles and 11 green marbles. Container F contains 37 grey marbles and 18 green marbles. How many green marbles and grey marbles must be moved from Container F to put into Container E so that 50% of the marbles in Container A are grey and 75% of the marbles in Container F are grey?
|
Container E |
Container F |
|
Grey marbles |
Green marbles |
Grey marbles |
Green marbles |
Before |
14 |
11 |
37 |
18 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of grey marbles = 14 + 37 = 51
Number of green marbles = 11 + 18 = 29
1 u + 3 p = 51 --- (1)
1 u + 1 p = 29 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 51 - 29
3 p - 1 p = 22
2 p = 22
1 p = 22 ÷ 2 = 11
From (2):
1 u + 1 p = 29
1 u + 1 x 11 = 29
1 u + 11 = 29
1 u = 29 - 11 = 18
Number of green marbles to be moved from Container F to Container E
= 18 - 1 p
= 18 - 1 x 11
= 18 - 11
= 7
Number of grey marbles to be moved from Container F to Container E
= 1 u - 14
= 18 - 14
= 4
Total number of green and grey marbles to be moved from Container F to Container E
= 7 + 4
= 11
Answer(s): 11