Lucy had 35 as many stickers as Xandra. The sum of the number of stickers Lucy and Xandra had was the same as the number of stickers that Winnie had. After trading, Winnie gave 20% of her stickers to Lucy and received 40% of Xandra's stickers. After that, Xandra 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 Lucy's and Winnie's stickers in the end.
| |
Lucy |
Winnie |
Xandra |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.6 u |
8.4 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of stickers that Lucy and Xandra had at first
= 3 u + 5 u
= 8 u
Number of stickers that Winnie had at first = 8 u
Number of stickers that Winnie gave to Lucy
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of stickers that Winnie received from Xandra
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of stickers that Xandra increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of stickers that Lucy and Winnie had in the end
= 4.6 u + 8.4 u - 0.6 u
= 12.4 u
In the end
Xandra : Lucy and Winnie
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
