Dana had 45 as many cards as Shiyun. The sum of the number of cards Dana and Shiyun had was the same as the number of cards that Julie had. After trading, Julie gave 10% of her cards to Dana and received 40% of Shiyun's cards. After that, Shiyun continued to trade and increased her number of cards in the end by 10%, find the ratio of her number of cards to the sum of Dana's and Julie's cards in the end.
| |
Dana |
Julie |
Shiyun |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.9 u |
10.1 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of cards that Dana and Shiyun had at first
= 4 u + 5 u
= 9 u
Number of cards that Julie had at first = 9 u
Number of cards that Julie gave to Dana
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of cards that Julie received from Shiyun
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of cards that Shiyun increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of cards that Dana and Julie had in the end
= 4.9 u + 10.1 u - 0.3 u
= 14.7 u
In the end
Shiyun : Dana and Julie
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
