Roshel had 45 as many beads as Fiona. The sum of the number of beads Roshel and Fiona had was the same as the number of beads that Kathy had. After trading, Kathy gave 30% of her beads to Roshel and received 40% of Fiona's beads. After that, Fiona continued to trade and increased her number of beads in the end by 10%, find the ratio of her number of beads to the sum of Roshel's and Kathy's beads in the end.
| |
Roshel |
Kathy |
Fiona |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of beads that Roshel and Fiona had at first
= 4 u + 5 u
= 9 u
Number of beads that Kathy had at first = 9 u
Number of beads that Kathy gave to Roshel
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Kathy received from Fiona
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Fiona increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of beads that Roshel and Kathy had in the end
= 6.7 u + 8.3 u - 0.3 u
= 14.7 u
In the end
Fiona : Roshel and Kathy
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
