Esther had 45 as many beads as Betty. The sum of the number of beads Esther and Betty had was the same as the number of beads that Joelle had. After trading, Joelle gave 30% of her beads to Esther and received 40% of Betty's beads. After that, Betty continued to trade and increased her number of beads in the end by 20%, find the ratio of her number of beads to the sum of Esther's and Joelle's beads in the end.
| |
Esther |
Joelle |
Betty |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of beads that Esther and Betty had at first
= 4 u + 5 u
= 9 u
Number of beads that Joelle had at first = 9 u
Number of beads that Joelle gave to Esther
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Joelle received from Betty
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Betty increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of beads that Esther and Joelle had in the end
= 6.7 u + 8.3 u - 0.6 u
= 14.4 u
In the end
Betty : Esther and Joelle
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
