Container M contains 16 red marbles and 9 brown marbles. Container N contains 49 red marbles and 26 brown marbles. How many brown marbles and red marbles must be removed from Container N to put into Container M so that 50% of the marbles in Container A are red and 75% of the marbles in Container N are red?
|
Container M |
Container N |
|
Red marbles |
Brown marbles |
Red marbles |
Brown marbles |
Before |
16 |
9 |
49 |
26 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of red marbles = 16 + 49 = 65
Number of brown marbles = 9 + 26 = 35
1 u + 3 p = 65 --- (1)
1 u + 1 p = 35 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 65 - 35
3 p - 1 p = 30
2 p = 30
1 p = 30 ÷ 2 = 15
From (2):
1 u + 1 p = 35
1 u + 1 x 15 = 35
1 u + 15 = 35
1 u = 35 - 15 = 20
Number of brown marbles to be removed from Container N to Container M
= 26 - 1 p
= 26 - 1 x 15
= 26 - 15
= 11
Number of red marbles to be removed from Container N to Container M
= 1 u - 16
= 20 - 16
= 4
Total number of brown and red marbles to be removed from Container N to Container M
= 11 + 4
= 15
Answer(s): 15