Irene had 45 as many beads as Shannon. The sum of the number of beads Irene and Shannon had was the same as the number of beads that Erika had. After trading, Erika gave 30% of her beads to Irene and received 40% of Shannon's beads. After that, Shannon continued to trade and increased her number of beads in the end by 30%, find the ratio of her number of beads to the sum of Irene's and Erika's beads in the end.
| |
Irene |
Erika |
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 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
14.1 u |
3.9 u |
18 u |
Total number of beads that Irene and Shannon had at first
= 4 u + 5 u
= 9 u
Number of beads that Erika had at first = 9 u
Number of beads that Erika gave to Irene
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Erika 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
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of beads that Irene and Erika had in the end
= 6.7 u + 8.3 u - 0.9 u
= 14.1 u
In the end
Shannon : Irene and Erika
3.9 : 14.1
390 : 1410
13 : 47
Answer(s): 13 : 47
