Raeann had 45 as many erasers as Olivia. The sum of the number of erasers Raeann and Olivia had was the same as the number of erasers that Zoe had. After trading, Zoe gave 30% of her erasers to Raeann and received 20% of Olivia's erasers. After that, Olivia 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 Raeann's and Zoe's erasers in the end.
| |
Raeann |
Zoe |
Olivia |
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 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of erasers that Raeann and Olivia had at first
= 4 u + 5 u
= 9 u
Number of erasers that Zoe had at first = 9 u
Number of erasers that Zoe gave to Raeann
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of erasers that Zoe received from Olivia
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Olivia increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of erasers that Raeann and Zoe had in the end
= 6.7 u + 7.3 u - 1.2 u
= 12.8 u
In the end
Olivia : Raeann and Zoe
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
