Gem had 45 as many coins as Kathy. The sum of the number of coins Gem and Kathy had was the same as the number of coins that Anna had. After trading, Anna gave 20% of her coins to Gem and received 25% of Kathy's coins. After that, Kathy 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 Gem's and Anna's coins in the end.
| |
Gem |
Anna |
Kathy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
5.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of coins that Gem and Kathy had at first
= 4 u + 5 u
= 9 u
Number of coins that Anna had at first = 9 u
Number of coins that Anna gave to Gem
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of coins that Anna received from Kathy
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of coins that Kathy increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of coins that Gem and Anna had in the end
= 5.8 u + 8.45 u - 0.75 u
= 13.5 u
In the end
Kathy : Gem and Anna
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
