Gwen had 35 as many pens as Emily. The sum of the number of pens Gwen and Emily had was the same as the number of pens that Risa had. After trading, Risa gave 10% of her pens to Gwen and received 40% of Emily's pens. After that, Emily 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 Gwen's and Risa's pens in the end.
| |
Gwen |
Risa |
Emily |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
3.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of pens that Gwen and Emily had at first
= 3 u + 5 u
= 8 u
Number of pens that Risa had at first = 8 u
Number of pens that Risa gave to Gwen
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of pens that Risa received from Emily
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of pens that Emily increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of pens that Gwen and Risa had in the end
= 3.8 u + 9.2 u - 0.6 u
= 12.4 u
In the end
Emily : Gwen and Risa
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
