Kathy had 35 as many beads as Erika. The sum of the number of beads Kathy and Erika had was the same as the number of beads that Risa had. After trading, Risa gave 20% of her beads to Kathy and received 20% of Erika's beads. After that, Erika continued to trade and increased her number of beads in the end by 30%, find the ratio of her number of beads to the sum of Kathy's and Risa's beads in the end.
| |
Kathy |
Risa |
Erika |
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 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of beads that Kathy and Erika had at first
= 3 u + 5 u
= 8 u
Number of beads that Risa had at first = 8 u
Number of beads that Risa gave to Kathy
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of beads that Risa received from Erika
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Erika increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of beads that Kathy and Risa had in the end
= 4.6 u + 7.4 u - 1.2 u
= 10.8 u
In the end
Erika : Kathy and Risa
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
