Gem had 45 as many erasers as Hilda. The sum of the number of erasers Gem and Hilda had was the same as the number of erasers that Nora had. After trading, Nora gave 30% of her erasers to Gem and received 20% of Hilda's erasers. After that, Hilda continued to trade and increased her number of erasers in the end by 20%, find the ratio of her number of erasers to the sum of Gem's and Nora's erasers in the end.
| |
Gem |
Nora |
Hilda |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of erasers that Gem and Hilda had at first
= 4 u + 5 u
= 9 u
Number of erasers that Nora had at first = 9 u
Number of erasers that Nora gave to Gem
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of erasers that Nora received from Hilda
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Hilda increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of erasers that Gem and Nora had in the end
= 6.7 u + 7.3 u - 0.8 u
= 13.2 u
In the end
Hilda : Gem and Nora
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
