Jade had 45 as many erasers as Xuan. The sum of the number of erasers Jade and Xuan had was the same as the number of erasers that Victoria had. After trading, Victoria gave 20% of her erasers to Jade and received 20% of Xuan's erasers. After that, Xuan 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 Jade's and Victoria's erasers in the end.
| |
Jade |
Victoria |
Xuan |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of erasers that Jade and Xuan had at first
= 4 u + 5 u
= 9 u
Number of erasers that Victoria had at first = 9 u
Number of erasers that Victoria gave to Jade
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of erasers that Victoria received from Xuan
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of erasers that Xuan increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of erasers that Jade and Victoria had in the end
= 5.8 u + 8.2 u - 0.8 u
= 13.2 u
In the end
Xuan : Jade and Victoria
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
