Diana had 45 as many stickers as Gabby. The sum of the number of stickers Diana and Gabby had was the same as the number of stickers that Wendy had. After trading, Wendy gave 20% of her stickers to Diana and received 10% of Gabby's stickers. After that, Gabby continued to trade and increased her number of stickers in the end by 10%, find the ratio of her number of stickers to the sum of Diana's and Wendy's stickers in the end.
| |
Diana |
Wendy |
Gabby |
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 |
- 0.45 u |
+ 0.45 u |
|
| After 2 |
13.05 u |
4.95 u |
18 u |
Total number of stickers that Diana and Gabby had at first
= 4 u + 5 u
= 9 u
Number of stickers that Wendy had at first = 9 u
Number of stickers that Wendy gave to Diana
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of stickers that Wendy received from Gabby
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of stickers that Gabby increased by when she continued to trade
= 10% x 4.5 u
=
10100 x 4.5 u
= 0.45 u
Number of stickers that Diana and Wendy had in the end
= 5.8 u + 7.7 u - 0.45 u
= 13.05 u
In the end
Gabby : Diana and Wendy
4.95 : 13.05
495 : 1305
11 : 29
Answer(s): 11 : 29
