Barbara had 45 as many cards as Roshel. The sum of the number of cards Barbara and Roshel had was the same as the number of cards that Emma had. After trading, Emma gave 30% of her cards to Barbara and received 30% of Roshel's cards. After that, Roshel 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 Barbara's and Emma's cards in the end.
| |
Barbara |
Emma |
Roshel |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
6.7 u |
7.8 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of cards that Barbara and Roshel had at first
= 4 u + 5 u
= 9 u
Number of cards that Emma had at first = 9 u
Number of cards that Emma gave to Barbara
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of cards that Emma received from Roshel
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of cards that Roshel increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of cards that Barbara and Emma had in the end
= 6.7 u + 7.8 u - 0.7 u
= 13.8 u
In the end
Roshel : Barbara and Emma
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
