Roshel had 45 as many pens as Tina. The sum of the number of pens Roshel and Tina had was the same as the number of pens that Pamela had. After trading, Pamela gave 30% of her pens to Roshel and received 20% of Tina's pens. After that, Tina continued to trade and increased her number of pens in the end by 30%, find the ratio of her number of pens to the sum of Roshel's and Pamela's pens in the end.
| |
Roshel |
Pamela |
Tina |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of pens that Roshel and Tina had at first
= 4 u + 5 u
= 9 u
Number of pens that Pamela had at first = 9 u
Number of pens that Pamela gave to Roshel
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of pens that Pamela received from Tina
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of pens that Tina increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of pens that Roshel and Pamela had in the end
= 6.7 u + 7.3 u - 1.2 u
= 12.8 u
In the end
Tina : Roshel and Pamela
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
