Container J contains 3 pink marbles and 15 blue marbles. Container K contains 39 pink marbles and 11 blue marbles. How many blue marbles and pink marbles must be transferred from Container K to put into Container J so that 50% of the marbles in Container A are pink and 75% of the marbles in Container K are pink?
|
Container J |
Container K |
|
Pink marbles |
Blue marbles |
Pink marbles |
Blue marbles |
Before |
3 |
15 |
39 |
11 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
3 p |
1 p |
50% =
50100 = 12
75% =
75100 = 34
Number of pink marbles = 3 + 39 = 42
Number of blue marbles = 15 + 11 = 26
1 u + 3 p = 42 --- (1)
1 u + 1 p = 26 ---(2)
(1) - (2)
(1 u + 3 p) - (1 u + 1 p) = 42 - 26
3 p - 1 p = 16
2 p = 16
1 p = 16 ÷ 2 = 8
From (2):
1 u + 1 p = 26
1 u + 1 x 8 = 26
1 u + 8 = 26
1 u = 26 - 8 = 18
Number of blue marbles to be transferred from Container K to Container J
= 11 - 1 p
= 11 - 1 x 8
= 11 - 8
= 3
Number of pink marbles to be transferred from Container K to Container J
= 1 u - 3
= 18 - 3
= 15
Total number of blue and pink marbles to be transferred from Container K to Container J
= 3 + 15
= 18
Answer(s): 18