Roshel had 35 as many cards as Anna. The sum of the number of cards Roshel and Anna had was the same as the number of cards that Dana had. After trading, Dana gave 30% of her cards to Roshel and received 25% of Anna's cards. After that, Anna continued to trade and increased her number of cards in the end by 20%, find the ratio of her number of cards to the sum of Roshel's and Dana's cards in the end.
| |
Roshel |
Dana |
Anna |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
5.4 u |
6.85 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of cards that Roshel and Anna had at first
= 3 u + 5 u
= 8 u
Number of cards that Dana had at first = 8 u
Number of cards that Dana gave to Roshel
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of cards that Dana received from Anna
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of cards that Anna increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of cards that Roshel and Dana had in the end
= 5.4 u + 6.85 u - 0.75 u
= 11.5 u
In the end
Anna : Roshel and Dana
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
