Linda had 45 as many stamps as Erika. The sum of the number of stamps Linda and Erika had was the same as the number of stamps that Yen had. After trading, Yen gave 30% of her stamps to Linda and received 10% of Erika's stamps. After that, Erika continued to trade and increased her number of stamps in the end by 30%, find the ratio of her number of stamps to the sum of Linda's and Yen's stamps in the end.
| |
Linda |
Yen |
Erika |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
6.7 u |
6.8 u |
4.5 u |
|
| Change 3 |
- 1.35 u |
+ 1.35 u |
|
| After 2 |
12.15 u |
5.85 u |
18 u |
Total number of stamps that Linda and Erika had at first
= 4 u + 5 u
= 9 u
Number of stamps that Yen had at first = 9 u
Number of stamps that Yen gave to Linda
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of stamps that Yen received from Erika
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of stamps that Erika increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of stamps that Linda and Yen had in the end
= 6.7 u + 6.8 u - 1.35 u
= 12.15 u
In the end
Erika : Linda and Yen
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
