Fiona had 45 as many stamps as Natalie. The sum of the number of stamps Fiona and Natalie had was the same as the number of stamps that Gillian had. After trading, Gillian gave 20% of her stamps to Fiona and received 20% of Natalie's stamps. After that, Natalie continued to trade and increased her number of stamps in the end by 30%, find the ratio of her number of stamps to the sum of Fiona's and Gillian's stamps in the end.
| |
Fiona |
Gillian |
Natalie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of stamps that Fiona and Natalie had at first
= 4 u + 5 u
= 9 u
Number of stamps that Gillian had at first = 9 u
Number of stamps that Gillian gave to Fiona
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of stamps that Gillian received from Natalie
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of stamps that Natalie increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of stamps that Fiona and Gillian had in the end
= 5.8 u + 8.2 u - 1.2 u
= 12.8 u
In the end
Natalie : Fiona and Gillian
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
