Diana had 45 as many cards as Raeann. The sum of the number of cards Diana and Raeann had was the same as the number of cards that Elyse had. After trading, Elyse gave 10% of her cards to Diana and received 20% of Raeann's cards. After that, Raeann 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 Diana's and Elyse's cards in the end.
| |
Diana |
Elyse |
Raeann |
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 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of cards that Diana and Raeann had at first
= 4 u + 5 u
= 9 u
Number of cards that Elyse had at first = 9 u
Number of cards that Elyse gave to Diana
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of cards that Elyse received from Raeann
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of cards that Raeann increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of cards that Diana and Elyse had in the end
= 4.9 u + 9.1 u - 0.8 u
= 13.2 u
In the end
Raeann : Diana and Elyse
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
