Wendy had 35 as many erasers as Shannon. The sum of the number of erasers Wendy and Shannon had was the same as the number of erasers that Cindy had. After trading, Cindy gave 10% of her erasers to Wendy and received 20% of Shannon's erasers. After that, Shannon 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 Wendy's and Cindy's erasers in the end.
| |
Wendy |
Cindy |
Shannon |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
3.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of erasers that Wendy and Shannon had at first
= 3 u + 5 u
= 8 u
Number of erasers that Cindy had at first = 8 u
Number of erasers that Cindy gave to Wendy
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of erasers that Cindy received from Shannon
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Shannon increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of erasers that Wendy and Cindy had in the end
= 3.8 u + 8.2 u - 1.2 u
= 10.8 u
In the end
Shannon : Wendy and Cindy
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
