Winnie had 45 as many coins as Natalie. The sum of the number of coins Winnie and Natalie had was the same as the number of coins that Lucy had. After trading, Lucy gave 20% of her coins to Winnie and received 40% of Natalie's coins. After that, Natalie 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 Winnie's and Lucy's coins in the end.
| |
Winnie |
Lucy |
Natalie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of coins that Winnie and Natalie had at first
= 4 u + 5 u
= 9 u
Number of coins that Lucy had at first = 9 u
Number of coins that Lucy gave to Winnie
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of coins that Lucy received from Natalie
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of coins that Natalie increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of coins that Winnie and Lucy had in the end
= 5.8 u + 9.2 u - 0.3 u
= 14.7 u
In the end
Natalie : Winnie and Lucy
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
