Winnie had 45 as many pens as Marion. The sum of the number of pens Winnie and Marion had was the same as the number of pens that Yoko had. After trading, Yoko gave 20% of her pens to Winnie and received 10% of Marion's pens. After that, Marion continued to trade and increased her number of pens in the end by 10%, find the ratio of her number of pens to the sum of Winnie's and Yoko's pens in the end.
| |
Winnie |
Yoko |
Marion |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 u |
4.5 u |
|
| Change 3 |
- 0.45 u |
+ 0.45 u |
|
| After 2 |
13.05 u |
4.95 u |
18 u |
Total number of pens that Winnie and Marion had at first
= 4 u + 5 u
= 9 u
Number of pens that Yoko had at first = 9 u
Number of pens that Yoko gave to Winnie
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of pens that Yoko received from Marion
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of pens that Marion increased by when she continued to trade
= 10% x 4.5 u
=
10100 x 4.5 u
= 0.45 u
Number of pens that Winnie and Yoko had in the end
= 5.8 u + 7.7 u - 0.45 u
= 13.05 u
In the end
Marion : Winnie and Yoko
4.95 : 13.05
495 : 1305
11 : 29
Answer(s): 11 : 29
