Dana had 45 as many cards as Diana. The sum of the number of cards Dana and Diana had was the same as the number of cards that Gem had. After trading, Gem gave 30% of her cards to Dana and received 10% of Diana's cards. After that, Diana 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 Gem's cards in the end.
| |
Dana |
Gem |
Diana |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
6.7 u |
6.8 u |
4.5 u |
|
| Change 3 |
- 0.45 u |
+ 0.45 u |
|
| After 2 |
13.05 u |
4.95 u |
18 u |
Total number of cards that Dana and Diana had at first
= 4 u + 5 u
= 9 u
Number of cards that Gem had at first = 9 u
Number of cards that Gem gave to Dana
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of cards that Gem received from Diana
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of cards that Diana increased by when she continued to trade
= 10% x 4.5 u
=
10100 x 4.5 u
= 0.45 u
Number of cards that Dana and Gem had in the end
= 6.7 u + 6.8 u - 0.45 u
= 13.05 u
In the end
Diana : Dana and Gem
4.95 : 13.05
495 : 1305
11 : 29
Answer(s): 11 : 29
