Hilda had 35 as many pens as Gillian. The sum of the number of pens Hilda and Gillian had was the same as the number of pens that Lynn had. After trading, Lynn gave 10% of her pens to Hilda and received 25% of Gillian's pens. After that, Gillian 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 Hilda's and Lynn's pens in the end.
| |
Hilda |
Lynn |
Gillian |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
3.8 u |
8.45 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 Hilda and Gillian had at first
= 3 u + 5 u
= 8 u
Number of pens that Lynn had at first = 8 u
Number of pens that Lynn gave to Hilda
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of pens that Lynn received from Gillian
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of pens that Gillian increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of pens that Hilda and Lynn had in the end
= 3.8 u + 8.45 u - 0.75 u
= 11.5 u
In the end
Gillian : Hilda and Lynn
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
