Tiffany had 45 as many stamps as Opal. The sum of the number of stamps Tiffany and Opal had was the same as the number of stamps that Zoe had. After trading, Zoe gave 10% of her stamps to Tiffany and received 40% of Opal's stamps. After that, Opal 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 Tiffany's and Zoe's stamps in the end.
| |
Tiffany |
Zoe |
Opal |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.9 u |
10.1 u |
3 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
14.1 u |
3.9 u |
18 u |
Total number of stamps that Tiffany and Opal had at first
= 4 u + 5 u
= 9 u
Number of stamps that Zoe had at first = 9 u
Number of stamps that Zoe gave to Tiffany
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of stamps that Zoe received from Opal
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of stamps that Opal increased by when she continued to trade
= 30% x 3 u
=
30100 x 3 u
= 0.9 u
Number of stamps that Tiffany and Zoe had in the end
= 4.9 u + 10.1 u - 0.9 u
= 14.1 u
In the end
Opal : Tiffany and Zoe
3.9 : 14.1
390 : 1410
13 : 47
Answer(s): 13 : 47
