Penelope had 45 as many coins as Esther. The sum of the number of coins Penelope and Esther had was the same as the number of coins that Olivia had. After trading, Olivia gave 10% of her coins to Penelope and received 10% of Esther's coins. After that, Esther 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 Penelope's and Olivia's coins in the end.
| |
Penelope |
Olivia |
Esther |
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 |
- 1.35 u |
+ 1.35 u |
|
| After 2 |
12.15 u |
5.85 u |
18 u |
Total number of coins that Penelope and Esther had at first
= 4 u + 5 u
= 9 u
Number of coins that Olivia had at first = 9 u
Number of coins that Olivia gave to Penelope
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of coins that Olivia received from Esther
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of coins that Esther increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of coins that Penelope and Olivia had in the end
= 4.9 u + 8.6 u - 1.35 u
= 12.15 u
In the end
Esther : Penelope and Olivia
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
