Xuan had 45 as many beads as Shannon. The sum of the number of beads Xuan and Shannon had was the same as the number of beads that Tammy had. After trading, Tammy gave 30% of her beads to Xuan and received 40% of Shannon's beads. After that, Shannon continued to trade and increased her number of beads in the end by 10%, find the ratio of her number of beads to the sum of Xuan's and Tammy's beads in the end.
|
Xuan |
Tammy |
Shannon |
Total |
Before |
4 u |
9 u |
5 u |
18 u |
Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
Change 2 |
|
+ 2 u |
- 2 u |
|
After 1 |
6.7 u |
8.3 u |
3 u |
|
Change 3 |
- 0.3 u |
+ 0.3 u |
|
After 2 |
14.7 u |
3.3 u |
18 u |
Total number of beads that Xuan and Shannon had at first
= 4 u + 5 u
= 9 u
Number of beads that Tammy had at first = 9 u
Number of beads that Tammy gave to Xuan
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of beads that Tammy received from Shannon
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of beads that Shannon increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of beads that Xuan and Tammy had in the end
= 6.7 u + 8.3 u - 0.3 u
= 14.7 u
In the end
Shannon : Xuan and Tammy
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49