Shiyun had 35 as many erasers as Hazel. The sum of the number of erasers Shiyun and Hazel had was the same as the number of erasers that Min had. After trading, Min gave 10% of her erasers to Shiyun and received 25% of Hazel's erasers. After that, Hazel 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 Shiyun's and Min's erasers in the end.
| |
Shiyun |
Min |
Hazel |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
3.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of erasers that Shiyun and Hazel had at first
= 3 u + 5 u
= 8 u
Number of erasers that Min had at first = 8 u
Number of erasers that Min gave to Shiyun
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of erasers that Min received from Hazel
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of erasers that Hazel increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of erasers that Shiyun and Min had in the end
= 3.8 u + 8.45 u - 0.75 u
= 11.5 u
In the end
Hazel : Shiyun and Min
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
