Xuan had 45 as many erasers as Abi. The sum of the number of erasers Xuan and Abi had was the same as the number of erasers that Mary had. After trading, Mary gave 10% of her erasers to Xuan and received 30% of Abi's erasers. After that, Abi 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 Xuan's and Mary's erasers in the end.
| |
Xuan |
Mary |
Abi |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
4.9 u |
9.6 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of erasers that Xuan and Abi had at first
= 4 u + 5 u
= 9 u
Number of erasers that Mary had at first = 9 u
Number of erasers that Mary gave to Xuan
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of erasers that Mary received from Abi
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of erasers that Abi increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of erasers that Xuan and Mary had in the end
= 4.9 u + 9.6 u - 0.7 u
= 13.8 u
In the end
Abi : Xuan and Mary
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
