Anna had 45 as many beads as Fanny. The sum of the number of beads Anna and Fanny had was the same as the number of beads that Winnie had. After trading, Winnie gave 10% of her beads to Anna and received 40% of Fanny's beads. After that, Fanny continued to trade and increased her number of beads in the end by 20%, find the ratio of her number of beads to the sum of Anna's and Winnie's beads in the end.
| |
Anna |
Winnie |
Fanny |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.9 u |
10.1 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of beads that Anna and Fanny had at first
= 4 u + 5 u
= 9 u
Number of beads that Winnie had at first = 9 u
Number of beads that Winnie gave to Anna
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of beads that Winnie received from Fanny
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Fanny increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of beads that Anna and Winnie had in the end
= 4.9 u + 10.1 u - 0.6 u
= 14.4 u
In the end
Fanny : Anna and Winnie
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
