Barbara had 45 as many pens as Jean. The sum of the number of pens Barbara and Jean had was the same as the number of pens that Min had. After trading, Min gave 10% of her pens to Barbara and received 20% of Jean's pens. After that, Jean 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 Barbara's and Min's pens in the end.
| |
Barbara |
Min |
Jean |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of pens that Barbara and Jean had at first
= 4 u + 5 u
= 9 u
Number of pens that Min had at first = 9 u
Number of pens that Min gave to Barbara
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of pens that Min received from Jean
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of pens that Jean increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of pens that Barbara and Min had in the end
= 4.9 u + 9.1 u - 0.8 u
= 13.2 u
In the end
Jean : Barbara and Min
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
