Erika had 45 as many pens as Gem. The sum of the number of pens Erika and Gem had was the same as the number of pens that Emily had. After trading, Emily gave 30% of her pens to Erika and received 40% of Gem's pens. After that, Gem 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 Erika's and Emily's pens in the end.
| |
Erika |
Emily |
Gem |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
14.1 u |
3.9 u |
18 u |
Total number of pens that Erika and Gem had at first
= 4 u + 5 u
= 9 u
Number of pens that Emily had at first = 9 u
Number of pens that Emily gave to Erika
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of pens that Emily received from Gem
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of pens that Gem increased by when she continued to trade
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of pens that Erika and Emily had in the end
= 6.7 u + 8.3 u - 0.9 u
= 14.1 u
In the end
Gem : Erika and Emily
3.9 : 14.1
390 : 1410
13 : 47
Answer(s): 13 : 47
