Esther had 35 as many beads as Gwen. The sum of the number of beads Esther and Gwen had was the same as the number of beads that Winnie had. After trading, Winnie gave 10% of her beads to Esther and received 20% of Gwen's beads. After that, Gwen 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 Esther's and Winnie's beads in the end.
| |
Esther |
Winnie |
Gwen |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
3.8 u |
8.2 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 Esther and Gwen had at first
= 3 u + 5 u
= 8 u
Number of beads that Winnie had at first = 8 u
Number of beads that Winnie gave to Esther
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of beads that Winnie received from Gwen
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of beads that Gwen increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of beads that Esther and Winnie had in the end
= 3.8 u + 8.2 u - 1.2 u
= 10.8 u
In the end
Gwen : Esther and Winnie
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
