Emma had 35 as many erasers as Risa. The sum of the number of erasers Emma and Risa had was the same as the number of erasers that Zara had. After trading, Zara gave 20% of her erasers to Emma and received 25% of Risa's erasers. After that, Risa 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 Emma's and Zara's erasers in the end.
| |
Emma |
Zara |
Risa |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
4.6 u |
7.65 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of erasers that Emma and Risa had at first
= 3 u + 5 u
= 8 u
Number of erasers that Zara had at first = 8 u
Number of erasers that Zara gave to Emma
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of erasers that Zara received from Risa
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of erasers that Risa increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of erasers that Emma and Zara had in the end
= 4.6 u + 7.65 u - 0.75 u
= 11.5 u
In the end
Risa : Emma and Zara
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
