Hazel had 45 as many coins as Kimberly. The sum of the number of coins Hazel and Kimberly had was the same as the number of coins that Eva had. After trading, Eva gave 20% of her coins to Hazel and received 40% of Kimberly's coins. After that, Kimberly 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 Hazel's and Eva's coins in the end.
| |
Hazel |
Eva |
Kimberly |
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 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of coins that Hazel and Kimberly had at first
= 4 u + 5 u
= 9 u
Number of coins that Eva had at first = 9 u
Number of coins that Eva gave to Hazel
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of coins that Eva received from Kimberly
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of coins that Kimberly increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of coins that Hazel and Eva had in the end
= 5.8 u + 9.2 u - 0.6 u
= 14.4 u
In the end
Kimberly : Hazel and Eva
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
