Dana had 35 as many erasers as Xylia. The sum of the number of erasers Dana and Xylia had was the same as the number of erasers that Pamela had. After trading, Pamela gave 20% of her erasers to Dana and received 20% of Xylia's erasers. After that, Xylia 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 Dana's and Pamela's erasers in the end.
| |
Dana |
Pamela |
Xylia |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.6 u |
7.4 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of erasers that Dana and Xylia had at first
= 3 u + 5 u
= 8 u
Number of erasers that Pamela had at first = 8 u
Number of erasers that Pamela gave to Dana
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of erasers that Pamela received from Xylia
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Xylia increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of erasers that Dana and Pamela had in the end
= 4.6 u + 7.4 u - 1.2 u
= 10.8 u
In the end
Xylia : Dana and Pamela
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
