Container K contains 11 blue beads and 17 silver beads. Container L contains 40 blue beads and 10 silver beads. How many silver beads and blue beads must be removed from Container L to put into Container K so that 50% of the beads in Container A are blue and 80% of the beads in Container L are blue?
|
Container K |
Container L |
|
Blue beads |
Silver beads |
Blue beads |
Silver beads |
Before |
11 |
17 |
40 |
10 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
4 p |
1 p |
50% =
50100 = 12
80% =
80100 = 45
Number of blue beads = 11 + 40 = 51
Number of silver beads = 17 + 10 = 27
1 u + 4 p = 51 --- (1)
1 u + 1 p = 27 ---(2)
(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 51 - 27
4 p - 1 p = 24
3 p = 24
1 p = 24 ÷ 3 = 8
From (2):
1 u + 1 p = 27
1 u + 1 x 8 = 27
1 u + 8 = 27
1 u = 27 - 8 = 19
Number of silver beads to be removed from Container L to Container K
= 10 - 1 p
= 10 - 1 x 8
= 10 - 8
= 2
Number of blue beads to be removed from Container L to Container K
= 1 u - 11
= 19 - 11
= 8
Total number of silver and blue beads to be removed from Container L to Container K
= 2 + 8
= 10
Answer(s): 10