Fiona had 45 as many beads as Shannon. The sum of the number of beads Fiona and Shannon had was the same as the number of beads that Pamela had. After trading, Pamela gave 30% of her beads to Fiona and received 40% of Shannon's beads. After that, Shannon 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 Fiona's and Pamela's beads in the end.
| |
Fiona |
Pamela |
Shannon |
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 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of beads that Fiona and Shannon had at first
= 4 u + 5 u
= 9 u
Number of beads that Pamela had at first = 9 u
Number of beads that Pamela gave to Fiona
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Pamela received from Shannon
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Shannon increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of beads that Fiona and Pamela had in the end
= 6.7 u + 8.3 u - 0.6 u
= 14.4 u
In the end
Shannon : Fiona and Pamela
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
