Gwen had 45 as many pens as Kylie. The sum of the number of pens Gwen and Kylie had was the same as the number of pens that Xandra had. After trading, Xandra gave 30% of her pens to Gwen and received 40% of Kylie's pens. After that, Kylie continued to trade and increased her number of pens in the end by 10%, find the ratio of her number of pens to the sum of Gwen's and Xandra's pens in the end.
| |
Gwen |
Xandra |
Kylie |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of pens that Gwen and Kylie had at first
= 4 u + 5 u
= 9 u
Number of pens that Xandra had at first = 9 u
Number of pens that Xandra gave to Gwen
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of pens that Xandra received from Kylie
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of pens that Kylie increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of pens that Gwen and Xandra had in the end
= 6.7 u + 8.3 u - 0.3 u
= 14.7 u
In the end
Kylie : Gwen and Xandra
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
