Vanessa had 45 as many cards as Fanny. The sum of the number of cards Vanessa and Fanny had was the same as the number of cards that Natalie had. After trading, Natalie gave 10% of her cards to Vanessa and received 20% of Fanny's cards. After that, Fanny continued to trade and increased her number of cards in the end by 30%, find the ratio of her number of cards to the sum of Vanessa's and Natalie's cards in the end.
| |
Vanessa |
Natalie |
Fanny |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of cards that Vanessa and Fanny had at first
= 4 u + 5 u
= 9 u
Number of cards that Natalie had at first = 9 u
Number of cards that Natalie gave to Vanessa
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of cards that Natalie received from Fanny
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of cards that Fanny increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of cards that Vanessa and Natalie had in the end
= 4.9 u + 9.1 u - 1.2 u
= 12.8 u
In the end
Fanny : Vanessa and Natalie
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
