Box T contains 4 brown beads and 9 silver beads. Box U contains 57 brown beads and 16 silver beads. How many silver beads and brown beads must be removed from Box U to put into Box T so that 50% of the beads in Box A are brown and 80% of the beads in Box U are brown?
|
Box T |
Box U |
|
Brown beads |
Silver beads |
Brown beads |
Silver beads |
Before |
4 |
9 |
57 |
16 |
Change |
+ ? |
+ ? |
- ? |
- ? |
After |
1 u |
1 u |
4 p |
1 p |
50% =
50100 = 12
80% =
80100 = 45
Number of brown beads = 4 + 57 = 61
Number of silver beads = 9 + 16 = 25
1 u + 4 p = 61 --- (1)
1 u + 1 p = 25 ---(2)
(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 61 - 25
4 p - 1 p = 36
3 p = 36
1 p = 36 ÷ 3 = 12
From (2):
1 u + 1 p = 25
1 u + 1 x 12 = 25
1 u + 12 = 25
1 u = 25 - 12 = 13
Number of silver beads to be removed from Box U to Box T
= 16 - 1 p
= 16 - 1 x 12
= 16 - 12
= 4
Number of brown beads to be removed from Box U to Box T
= 1 u - 4
= 13 - 4
= 9
Total number of silver and brown beads to be removed from Box U to Box T
= 4 + 9
= 13
Answer(s): 13