Hazel had 45 as many pens as Lynn. The sum of the number of pens Hazel and Lynn had was the same as the number of pens that Wendy had. After trading, Wendy gave 20% of her pens to Hazel 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 Hazel's and Wendy's pens in the end.
| |
Hazel |
Wendy |
Lynn |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 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 Hazel and Lynn had at first
= 4 u + 5 u
= 9 u
Number of pens that Wendy had at first = 9 u
Number of pens that Wendy gave to Hazel
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of pens that Wendy 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 Hazel and Wendy had in the end
= 5.8 u + 8.2 u - 1.2 u
= 12.8 u
In the end
Lynn : Hazel and Wendy
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
