Shannon had 45 as many coins as Esther. The sum of the number of coins Shannon and Esther had was the same as the number of coins that Risa had. After trading, Risa gave 30% of her coins to Shannon and received 20% of Esther's coins. After that, Esther continued to trade and increased her number of coins in the end by 10%, find the ratio of her number of coins to the sum of Shannon's and Risa's coins in the end.
| |
Shannon |
Risa |
Esther |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
13.6 u |
4.4 u |
18 u |
Total number of coins that Shannon and Esther had at first
= 4 u + 5 u
= 9 u
Number of coins that Risa had at first = 9 u
Number of coins that Risa gave to Shannon
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of coins that Risa received from Esther
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of coins that Esther increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of coins that Shannon and Risa had in the end
= 6.7 u + 7.3 u - 0.4 u
= 13.6 u
In the end
Esther : Shannon and Risa
4.4 : 13.6
440 : 1360
11 : 34
Answer(s): 11 : 34
