Elyse had 35 as many marbles as Fanny. The sum of the number of marbles Elyse and Fanny had was the same as the number of marbles that Gabby had. After trading, Gabby gave 20% of her marbles to Elyse and received 20% of Fanny's marbles. After that, Fanny continued to trade and increased her number of marbles in the end by 30%, find the ratio of her number of marbles to the sum of Elyse's and Gabby's marbles in the end.
| |
Elyse |
Gabby |
Fanny |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.6 u |
7.4 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of marbles that Elyse and Fanny had at first
= 3 u + 5 u
= 8 u
Number of marbles that Gabby had at first = 8 u
Number of marbles that Gabby gave to Elyse
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of marbles that Gabby received from Fanny
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Fanny increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of marbles that Elyse and Gabby had in the end
= 4.6 u + 7.4 u - 1.2 u
= 10.8 u
In the end
Fanny : Elyse and Gabby
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
