Diana had 45 as many erasers as Eva. The sum of the number of erasers Diana and Eva had was the same as the number of erasers that Jen had. After trading, Jen gave 10% of her erasers to Diana and received 20% of Eva's erasers. After that, Eva continued to trade and increased her number of erasers in the end by 30%, find the ratio of her number of erasers to the sum of Diana's and Jen's erasers in the end.
| |
Diana |
Jen |
Eva |
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 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of erasers that Diana and Eva had at first
= 4 u + 5 u
= 9 u
Number of erasers that Jen had at first = 9 u
Number of erasers that Jen gave to Diana
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of erasers that Jen received from Eva
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Eva increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of erasers that Diana and Jen had in the end
= 4.9 u + 9.1 u - 1.2 u
= 12.8 u
In the end
Eva : Diana and Jen
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
