Betty had 35 as many erasers as Nora. The sum of the number of erasers Betty and Nora had was the same as the number of erasers that Fiona had. After trading, Fiona gave 30% of her erasers to Betty and received 20% of Nora's erasers. After that, Nora continued to trade and increased her number of erasers in the end by 30%, find the ratio of her number of erasers to the sum of Betty's and Fiona's erasers in the end.
| |
Betty |
Fiona |
Nora |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.4 u |
6.6 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of erasers that Betty and Nora had at first
= 3 u + 5 u
= 8 u
Number of erasers that Fiona had at first = 8 u
Number of erasers that Fiona gave to Betty
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of erasers that Fiona received from Nora
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Nora increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of erasers that Betty and Fiona had in the end
= 5.4 u + 6.6 u - 1.2 u
= 10.8 u
In the end
Nora : Betty and Fiona
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
