Irene had 45 as many coins as Winnie. The sum of the number of coins Irene and Winnie had was the same as the number of coins that Joelle had. After trading, Joelle gave 10% of her coins to Irene and received 10% of Winnie's coins. After that, Winnie continued to trade and increased her number of coins in the end by 20%, find the ratio of her number of coins to the sum of Irene's and Joelle's coins in the end.
| |
Irene |
Joelle |
Winnie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
4.9 u |
8.6 u |
4.5 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
12.6 u |
5.4 u |
18 u |
Total number of coins that Irene and Winnie had at first
= 4 u + 5 u
= 9 u
Number of coins that Joelle had at first = 9 u
Number of coins that Joelle gave to Irene
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of coins that Joelle received from Winnie
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of coins that Winnie increased by when she continued to trade
= 20% x 4.5 u
=
20100 x 4.5 u
= 0.9 u
Number of coins that Irene and Joelle had in the end
= 4.9 u + 8.6 u - 0.9 u
= 12.6 u
In the end
Winnie : Irene and Joelle
5.4 : 12.6
540 : 1260
3 : 7
Answer(s): 3 : 7
