Olivia had 45 as many coins as Gabby. The sum of the number of coins Olivia and Gabby had was the same as the number of coins that Kimberly had. After trading, Kimberly gave 30% of her coins to Olivia and received 10% of Gabby's coins. After that, Gabby 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 Olivia's and Kimberly's coins in the end.
| |
Olivia |
Kimberly |
Gabby |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
6.7 u |
6.8 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 Olivia and Gabby had at first
= 4 u + 5 u
= 9 u
Number of coins that Kimberly had at first = 9 u
Number of coins that Kimberly gave to Olivia
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of coins that Kimberly received from Gabby
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of coins that Gabby increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of coins that Olivia and Kimberly had in the end
= 6.7 u + 6.8 u - 1.35 u
= 12.15 u
In the end
Gabby : Olivia and Kimberly
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
