Kimberly had 35 as many pens as Wendy. The sum of the number of pens Kimberly and Wendy had was the same as the number of pens that Lucy had. After trading, Lucy gave 20% of her pens to Kimberly and received 25% of Wendy's pens. After that, Wendy continued to trade and increased her number of pens in the end by 20%, find the ratio of her number of pens to the sum of Kimberly's and Lucy's pens in the end.
| |
Kimberly |
Lucy |
Wendy |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
4.6 u |
7.65 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of pens that Kimberly and Wendy had at first
= 3 u + 5 u
= 8 u
Number of pens that Lucy had at first = 8 u
Number of pens that Lucy gave to Kimberly
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of pens that Lucy received from Wendy
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of pens that Wendy increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of pens that Kimberly and Lucy had in the end
= 4.6 u + 7.65 u - 0.75 u
= 11.5 u
In the end
Wendy : Kimberly and Lucy
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
