Anna had 45 as many pens as Lynn. The sum of the number of pens Anna and Lynn had was the same as the number of pens that Irene had. After trading, Irene gave 30% of her pens to Anna and received 20% of Lynn's pens. After that, Lynn continued to trade and increased her number of pens in the end by 30%, find the ratio of her number of pens to the sum of Anna's and Irene's pens in the end.
| |
Anna |
Irene |
Lynn |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of pens that Anna and Lynn had at first
= 4 u + 5 u
= 9 u
Number of pens that Irene had at first = 9 u
Number of pens that Irene gave to Anna
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of pens that Irene received from Lynn
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of pens that Lynn increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of pens that Anna and Irene had in the end
= 6.7 u + 7.3 u - 1.2 u
= 12.8 u
In the end
Lynn : Anna and Irene
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
