Jane had 45 as many stamps as Cathy. The sum of the number of stamps Jane and Cathy had was the same as the number of stamps that Xylia had. After trading, Xylia gave 20% of her stamps to Jane and received 10% of Cathy's stamps. After that, Cathy 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 Jane's and Xylia's stamps in the end.
| |
Jane |
Xylia |
Cathy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 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 Jane and Cathy had at first
= 4 u + 5 u
= 9 u
Number of stamps that Xylia had at first = 9 u
Number of stamps that Xylia gave to Jane
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of stamps that Xylia received from Cathy
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of stamps that Cathy increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of stamps that Jane and Xylia had in the end
= 5.8 u + 7.7 u - 1.35 u
= 12.15 u
In the end
Cathy : Jane and Xylia
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
