Anna had 45 as many stamps as Opal. The sum of the number of stamps Anna and Opal had was the same as the number of stamps that Gabby had. After trading, Gabby gave 10% of her stamps to Anna and received 20% of Opal's stamps. After that, Opal continued to trade and increased her number of stamps in the end by 10%, find the ratio of her number of stamps to the sum of Anna's and Gabby's stamps in the end.
| |
Anna |
Gabby |
Opal |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
13.6 u |
4.4 u |
18 u |
Total number of stamps that Anna and Opal had at first
= 4 u + 5 u
= 9 u
Number of stamps that Gabby had at first = 9 u
Number of stamps that Gabby gave to Anna
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of stamps that Gabby received from Opal
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of stamps that Opal increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of stamps that Anna and Gabby had in the end
= 4.9 u + 9.1 u - 0.4 u
= 13.6 u
In the end
Opal : Anna and Gabby
4.4 : 13.6
440 : 1360
11 : 34
Answer(s): 11 : 34
