Shiyun had 45 as many marbles as Xuan. The sum of the number of marbles Shiyun and Xuan had was the same as the number of marbles that Lucy had. After trading, Lucy gave 30% of her marbles to Shiyun and received 10% of Xuan's marbles. After that, Xuan continued to trade and increased her number of marbles in the end by 10%, find the ratio of her number of marbles to the sum of Shiyun's and Lucy's marbles in the end.
| |
Shiyun |
Lucy |
Xuan |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
6.7 u |
6.8 u |
4.5 u |
|
| Change 3 |
- 0.45 u |
+ 0.45 u |
|
| After 2 |
13.05 u |
4.95 u |
18 u |
Total number of marbles that Shiyun and Xuan had at first
= 4 u + 5 u
= 9 u
Number of marbles that Lucy had at first = 9 u
Number of marbles that Lucy gave to Shiyun
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of marbles that Lucy received from Xuan
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of marbles that Xuan increased by when she continued to trade
= 10% x 4.5 u
=
10100 x 4.5 u
= 0.45 u
Number of marbles that Shiyun and Lucy had in the end
= 6.7 u + 6.8 u - 0.45 u
= 13.05 u
In the end
Xuan : Shiyun and Lucy
4.95 : 13.05
495 : 1305
11 : 29
Answer(s): 11 : 29
