Julie had 45 as many stickers as Jane. The sum of the number of stickers Julie and Jane had was the same as the number of stickers that Penelope had. After trading, Penelope gave 20% of her stickers to Julie and received 40% of Jane's stickers. After that, Jane continued to trade and increased her number of stickers in the end by 20%, find the ratio of her number of stickers to the sum of Julie's and Penelope's stickers in the end.
| |
Julie |
Penelope |
Jane |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
5.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of stickers that Julie and Jane had at first
= 4 u + 5 u
= 9 u
Number of stickers that Penelope had at first = 9 u
Number of stickers that Penelope gave to Julie
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of stickers that Penelope received from Jane
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of stickers that Jane increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of stickers that Julie and Penelope had in the end
= 5.8 u + 9.2 u - 0.6 u
= 14.4 u
In the end
Jane : Julie and Penelope
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
