Erika had 45 as many coins as Sabrina. The sum of the number of coins Erika and Sabrina had was the same as the number of coins that Yen had. After trading, Yen gave 10% of her coins to Erika and received 40% of Sabrina's coins. After that, Sabrina 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 Erika's and Yen's coins in the end.
| |
Erika |
Yen |
Sabrina |
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 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
14.1 u |
3.9 u |
18 u |
Total number of coins that Erika and Sabrina had at first
= 4 u + 5 u
= 9 u
Number of coins that Yen had at first = 9 u
Number of coins that Yen gave to Erika
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of coins that Yen received from Sabrina
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of coins that Sabrina increased by when she continued to trade
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of coins that Erika and Yen had in the end
= 4.9 u + 10.1 u - 0.9 u
= 14.1 u
In the end
Sabrina : Erika and Yen
3.9 : 14.1
390 : 1410
13 : 47
Answer(s): 13 : 47
