Anna had 35 as many cards as Cindy. The sum of the number of cards Anna and Cindy had was the same as the number of cards that Irene had. After trading, Irene gave 20% of her cards to Anna and received 40% of Cindy's cards. After that, Cindy 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 Anna's and Irene's cards in the end.
| |
Anna |
Irene |
Cindy |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.6 u |
8.4 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of cards that Anna and Cindy had at first
= 3 u + 5 u
= 8 u
Number of cards that Irene had at first = 8 u
Number of cards that Irene gave to Anna
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of cards that Irene received from Cindy
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of cards that Cindy increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of cards that Anna and Irene had in the end
= 4.6 u + 8.4 u - 0.6 u
= 12.4 u
In the end
Cindy : Anna and Irene
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
