Container B contains 7 silver balls and 10 blue balls. Container C contains 44 silver balls and 17 blue balls. How many blue balls and silver balls must be moved from Container C to put into Container B so that 50% of the balls in Container A are silver and 75% of the balls in Container C are silver?
|
Container B |
Container C |
|
Silver balls |
Blue balls |
Silver balls |
Blue balls |
Before |
7 |
10 |
44 |
17 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of silver balls = 7 + 44 = 51
Number of blue balls = 10 + 17 = 27
1 u + 3 p = 51 --- (1)
1 u + 1 p = 27 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 51 - 27
3 p - 1 p = 24
2 p = 24
1 p = 24 ÷ 2 = 12
From (2):
1 u + 1 p = 27
1 u + 1 x 12 = 27
1 u + 12 = 27
1 u = 27 - 12 = 15
Number of blue balls to be moved from Container C to Container B
= 17 - 1 p
= 17 - 1 x 12
= 17 - 12
= 5
Number of silver balls to be moved from Container C to Container B
= 1 u - 7
= 15 - 7
= 8
Total number of blue and silver balls to be moved from Container C to Container B
= 5 + 8
= 13
Answer(s): 13