Erika had 45 as many erasers as Marion. The sum of the number of erasers Erika and Marion had was the same as the number of erasers that Nicole had. After trading, Nicole gave 10% of her erasers to Erika and received 20% of Marion's erasers. After that, Marion 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 Erika's and Nicole's erasers in the end.
| |
Erika |
Nicole |
Marion |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 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 Erika and Marion had at first
= 4 u + 5 u
= 9 u
Number of erasers that Nicole had at first = 9 u
Number of erasers that Nicole gave to Erika
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of erasers that Nicole received from Marion
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Marion increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of erasers that Erika and Nicole had in the end
= 4.9 u + 9.1 u - 0.8 u
= 13.2 u
In the end
Marion : Erika and Nicole
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
