Container A contains 3 blue balls and 17 yellow balls. Container B contains 40 blue balls and 8 yellow balls. How many yellow balls and blue balls must be moved from Container B to put into Container A so that 50% of the balls in Container A are blue and 80% of the balls in Container B are blue?
|
Container A |
Container B |
|
Blue balls |
Yellow balls |
Blue balls |
Yellow balls |
Before |
3 |
17 |
40 |
8 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
4 p |
1 p |
50% =
50100 = 12
80% =
80100 = 45
Number of blue balls = 3 + 40 = 43
Number of yellow balls = 17 + 8 = 25
1 u + 4 p = 43 --- (1)
1 u + 1 p = 25 ---(2)
(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 43 - 25
4 p - 1 p = 18
3 p = 18
1 p = 18 ÷ 3 = 6
From (2):
1 u + 1 p = 25
1 u + 1 x 6 = 25
1 u + 6 = 25
1 u = 25 - 6 = 19
Number of yellow balls to be moved from Container B to Container A
= 8 - 1 p
= 8 - 1 x 6
= 8 - 6
= 2
Number of blue balls to be moved from Container B to Container A
= 1 u - 3
= 19 - 3
= 16
Total number of yellow and blue balls to be moved from Container B to Container A
= 2 + 16
= 18
Answer(s): 18