Container K contains 6 green balls and 5 black balls. Container L contains 54 green balls and 25 black balls. How many black balls and green balls must be moved from Container L to put into Container K so that 50% of the balls in Container A are green and 80% of the balls in Container L are green?
|
Container K |
Container L |
|
Green balls |
Black balls |
Green balls |
Black balls |
Before |
6 |
5 |
54 |
25 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
4 p |
1 p |
50% =
50100 = 12
80% =
80100 = 45
Number of green balls = 6 + 54 = 60
Number of black balls = 5 + 25 = 30
1 u + 4 p = 60 --- (1)
1 u + 1 p = 30 ---(2)
(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 60 - 30
4 p - 1 p = 30
3 p = 30
1 p = 30 ÷ 3 = 10
From (2):
1 u + 1 p = 30
1 u + 1 x 10 = 30
1 u + 10 = 30
1 u = 30 - 10 = 20
Number of black balls to be moved from Container L to Container K
= 25 - 1 p
= 25 - 1 x 10
= 25 - 10
= 15
Number of green balls to be moved from Container L to Container K
= 1 u - 6
= 20 - 6
= 14
Total number of black and green balls to be moved from Container L to Container K
= 15 + 14
= 29
Answer(s): 29