Shiyun had 35 as many erasers as Barbara. The sum of the number of erasers Shiyun and Barbara had was the same as the number of erasers that Zara had. After trading, Zara gave 30% of her erasers to Shiyun and received 20% of Barbara's erasers. After that, Barbara continued to trade and increased her number of erasers in the end by 10%, find the ratio of her number of erasers to the sum of Shiyun's and Zara's erasers in the end.
| |
Shiyun |
Zara |
Barbara |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 2.4 u |
- 2.4 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.4 u |
6.6 u |
4 u |
|
| Change 3 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
11.6 u |
4.4 u |
16 u |
Total number of erasers that Shiyun and Barbara had at first
= 3 u + 5 u
= 8 u
Number of erasers that Zara had at first = 8 u
Number of erasers that Zara gave to Shiyun
= 30% x 8 u
=
30100 x 3 u
= 2.4 u
Number of erasers that Zara received from Barbara
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Barbara increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of erasers that Shiyun and Zara had in the end
= 5.4 u + 6.6 u - 0.4 u
= 11.6 u
In the end
Barbara : Shiyun and Zara
4.4 : 11.6
440 : 1160
11 : 29
Answer(s): 11 : 29
