Xuan had 45 as many coins as Eva. The sum of the number of coins Xuan and Eva had was the same as the number of coins that Shiyun had. After trading, Shiyun gave 30% of her coins to Xuan and received 40% of Eva's coins. After that, Eva continued to trade and increased her number of coins in the end by 30%, find the ratio of her number of coins to the sum of Xuan's and Shiyun's coins in the end.
| |
Xuan |
Shiyun |
Eva |
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 coins that Xuan and Eva had at first
= 4 u + 5 u
= 9 u
Number of coins that Shiyun had at first = 9 u
Number of coins that Shiyun gave to Xuan
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of coins that Shiyun received from Eva
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of coins that Eva increased by when she continued to trade
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of coins that Xuan and Shiyun had in the end
= 6.7 u + 8.3 u - 0.9 u
= 14.1 u
In the end
Eva : Xuan and Shiyun
3.9 : 14.1
390 : 1410
13 : 47
Answer(s): 13 : 47
