Min had 45 as many pens as Sarah. The sum of the number of pens Min and Sarah had was the same as the number of pens that Opal had. After trading, Opal gave 20% of her pens to Min and received 20% of Sarah's pens. After that, Sarah 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 Min's and Opal's pens in the end.
| |
Min |
Opal |
Sarah |
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 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of pens that Min and Sarah had at first
= 4 u + 5 u
= 9 u
Number of pens that Opal had at first = 9 u
Number of pens that Opal gave to Min
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of pens that Opal received from Sarah
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of pens that Sarah increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of pens that Min and Opal had in the end
= 5.8 u + 8.2 u - 0.8 u
= 13.2 u
In the end
Sarah : Min and Opal
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
