Container G contains 5 brown marbles and 11 silver marbles. Container H contains 103 brown marbles and 45 silver marbles. How many silver marbles and brown marbles must be moved from Container H to put into Container G so that 50% of the marbles in Container A are brown and 70% of the marbles in Container H are brown?
|
Container G |
Container H |
|
Brown marbles |
Silver marbles |
Brown marbles |
Silver marbles |
Before |
5 |
11 |
103 |
45 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
7 p |
3 p |
50% =
50100 = 12
70% =
70100 = 710
Number of brown marbles = 5 + 103 = 108
Number of silver marbles = 11 + 45 = 56
1 u + 7 p = 108 --- (1)
1 u + 3 p = 56 ---(2)
(1) - (2)
(1 u + 7 p) - (1 u + 3 p) = 108 - 56
7 p - 3 p = 52
4 p = 52
1 p = 52 ÷ 4 = 13
From (2):
1 u + 3 p = 56
1 u + 3 x 13 = 56
1 u + 39 = 56
1 u = 56 - 39 = 17
Number of silver marbles to be moved from Container H to Container G
= 45 - 3 p
= 45 - 3 x 13
= 45 - 39
= 6
Number of brown marbles to be moved from Container H to Container G
= 1 u - 5
= 17 - 5
= 12
Total number of silver and brown marbles to be moved from Container H to Container G
= 6 + 12
= 18
Answer(s): 18