Vanessa had 45 as many erasers as Penelope. The sum of the number of erasers Vanessa and Penelope had was the same as the number of erasers that Raeann had. After trading, Raeann gave 20% of her erasers to Vanessa and received 10% of Penelope's erasers. After that, Penelope 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 Vanessa's and Raeann's erasers in the end.
| |
Vanessa |
Raeann |
Penelope |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 u |
4.5 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
12.6 u |
5.4 u |
18 u |
Total number of erasers that Vanessa and Penelope had at first
= 4 u + 5 u
= 9 u
Number of erasers that Raeann had at first = 9 u
Number of erasers that Raeann gave to Vanessa
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of erasers that Raeann received from Penelope
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of erasers that Penelope increased by when she continued to trade
= 20% x 4.5 u
=
20100 x 4.5 u
= 0.9 u
Number of erasers that Vanessa and Raeann had in the end
= 5.8 u + 7.7 u - 0.9 u
= 12.6 u
In the end
Penelope : Vanessa and Raeann
5.4 : 12.6
540 : 1260
3 : 7
Answer(s): 3 : 7
