Container K contains 2 brown beads and 10 yellow beads. Container L contains 81 brown beads and 22 yellow beads. How many yellow beads and brown beads must be removed from Container L to put into Container K so that 50% of the beads in Container A are brown and 80% of the beads in Container L are brown?
|
Container K |
Container L |
|
Brown beads |
Yellow beads |
Brown beads |
Yellow beads |
Before |
2 |
10 |
81 |
22 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
4 p |
1 p |
50% =
50100 = 12
80% =
80100 = 45
Number of brown beads = 2 + 81 = 83
Number of yellow beads = 10 + 22 = 32
1 u + 4 p = 83 --- (1)
1 u + 1 p = 32 ---(2)
(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 83 - 32
4 p - 1 p = 51
3 p = 51
1 p = 51 ÷ 3 = 17
From (2):
1 u + 1 p = 32
1 u + 1 x 17 = 32
1 u + 17 = 32
1 u = 32 - 17 = 15
Number of yellow beads to be removed from Container L to Container K
= 22 - 1 p
= 22 - 1 x 17
= 22 - 17
= 5
Number of brown beads to be removed from Container L to Container K
= 1 u - 2
= 15 - 2
= 13
Total number of yellow and brown beads to be removed from Container L to Container K
= 5 + 13
= 18
Answer(s): 18