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