Julie had 45 as many buttons as Dana. The sum of the number of buttons Julie and Dana had was the same as the number of buttons that Xuan had. After trading, Xuan gave 10% of her buttons to Julie and received 20% of Dana's buttons. After that, Dana continued to trade and increased her number of buttons in the end by 30%, find the ratio of her number of buttons to the sum of Julie's and Xuan's buttons in the end.
| |
Julie |
Xuan |
Dana |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
12.8 u |
5.2 u |
18 u |
Total number of buttons that Julie and Dana had at first
= 4 u + 5 u
= 9 u
Number of buttons that Xuan had at first = 9 u
Number of buttons that Xuan gave to Julie
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of buttons that Xuan received from Dana
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of buttons that Dana increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of buttons that Julie and Xuan had in the end
= 4.9 u + 9.1 u - 1.2 u
= 12.8 u
In the end
Dana : Julie and Xuan
5.2 : 12.8
520 : 1280
13 : 32
Answer(s): 13 : 32
