Raeann had 45 as many cards as Julie. The sum of the number of cards Raeann and Julie had was the same as the number of cards that Hilda had. After trading, Hilda gave 20% of her cards to Raeann and received 25% of Julie's cards. After that, Julie 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 Raeann's and Hilda's cards in the end.
| |
Raeann |
Hilda |
Julie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
5.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of cards that Raeann and Julie had at first
= 4 u + 5 u
= 9 u
Number of cards that Hilda had at first = 9 u
Number of cards that Hilda gave to Raeann
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of cards that Hilda received from Julie
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of cards that Julie increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of cards that Raeann and Hilda had in the end
= 5.8 u + 8.45 u - 0.75 u
= 13.5 u
In the end
Julie : Raeann and Hilda
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
