Sarah had 35 as many pens as Shannon. The sum of the number of pens Sarah and Shannon had was the same as the number of pens that Erika had. After trading, Erika gave 30% of her pens to Sarah and received 40% of Shannon's pens. After that, Shannon 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 Sarah's and Erika's pens in the end.
| |
Sarah |
Erika |
Shannon |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.4 u |
7.6 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 Sarah and Shannon had at first
= 3 u + 5 u
= 8 u
Number of pens that Erika had at first = 8 u
Number of pens that Erika gave to Sarah
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of pens that Erika received from Shannon
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of pens that Shannon increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of pens that Sarah and Erika had in the end
= 5.4 u + 7.6 u - 0.6 u
= 12.4 u
In the end
Shannon : Sarah and Erika
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
