Rachel had 45 as many stamps as Risa. The sum of the number of stamps Rachel and Risa had was the same as the number of stamps that Mary had. After trading, Mary gave 10% of her stamps to Rachel and received 10% of Risa's stamps. After that, Risa 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 Rachel's and Mary's stamps in the end.
| |
Rachel |
Mary |
Risa |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
4.9 u |
8.6 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 Rachel and Risa had at first
= 4 u + 5 u
= 9 u
Number of stamps that Mary had at first = 9 u
Number of stamps that Mary gave to Rachel
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of stamps that Mary received from Risa
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of stamps that Risa increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of stamps that Rachel and Mary had in the end
= 4.9 u + 8.6 u - 1.35 u
= 12.15 u
In the end
Risa : Rachel and Mary
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
