Opal had 35 as many stamps as Emily. The sum of the number of stamps Opal and Emily had was the same as the number of stamps that Ivory had. After trading, Ivory gave 20% of her stamps to Opal and received 20% of Emily's stamps. After that, Emily 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 Opal's and Ivory's stamps in the end.
| |
Opal |
Ivory |
Emily |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.6 u |
7.4 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
11.6 u |
4.4 u |
16 u |
Total number of stamps that Opal and Emily had at first
= 3 u + 5 u
= 8 u
Number of stamps that Ivory had at first = 8 u
Number of stamps that Ivory gave to Opal
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of stamps that Ivory received from Emily
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of stamps that Emily increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of stamps that Opal and Ivory had in the end
= 4.6 u + 7.4 u - 0.4 u
= 11.6 u
In the end
Emily : Opal and Ivory
4.4 : 11.6
440 : 1160
11 : 29
Answer(s): 11 : 29
