Container U contains 10 green balls and 12 yellow balls. Container V contains 15 green balls and 7 yellow balls. How many yellow balls and green balls must be moved from Container V to put into Container U so that 50% of the balls in Container A are green and 75% of the balls in Container V are green?
|
Container U |
Container V |
|
Green balls |
Yellow balls |
Green balls |
Yellow balls |
Before |
10 |
12 |
15 |
7 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of green balls = 10 + 15 = 25
Number of yellow balls = 12 + 7 = 19
1 u + 3 p = 25 --- (1)
1 u + 1 p = 19 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 25 - 19
3 p - 1 p = 6
2 p = 6
1 p = 6 ÷ 2 = 3
From (2):
1 u + 1 p = 19
1 u + 1 x 3 = 19
1 u + 3 = 19
1 u = 19 - 3 = 16
Number of yellow balls to be moved from Container V to Container U
= 7 - 1 p
= 7 - 1 x 3
= 7 - 3
= 4
Number of green balls to be moved from Container V to Container U
= 1 u - 10
= 16 - 10
= 6
Total number of yellow and green balls to be moved from Container V to Container U
= 4 + 6
= 10
Answer(s): 10