Usha had 45 as many marbles as Gabby. The sum of the number of marbles Usha and Gabby had was the same as the number of marbles that Shiyun had. After trading, Shiyun gave 20% of her marbles to Usha and received 10% of Gabby's marbles. After that, Gabby continued to trade and increased her number of marbles in the end by 30%, find the ratio of her number of marbles to the sum of Usha's and Shiyun's marbles in the end.
| |
Usha |
Shiyun |
Gabby |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
5.8 u |
7.7 u |
4.5 u |
|
| Change 3 |
- 1.35 u |
+ 1.35 u |
|
| After 2 |
12.15 u |
5.85 u |
18 u |
Total number of marbles that Usha and Gabby had at first
= 4 u + 5 u
= 9 u
Number of marbles that Shiyun had at first = 9 u
Number of marbles that Shiyun gave to Usha
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of marbles that Shiyun received from Gabby
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of marbles that Gabby increased by when she continued to trade
= 30% x 4.5 u
=
30100 x 4.5 u
= 1.35 u
Number of marbles that Usha and Shiyun had in the end
= 5.8 u + 7.7 u - 1.35 u
= 12.15 u
In the end
Gabby : Usha and Shiyun
5.85 : 12.15
585 : 1215
13 : 27
Answer(s): 13 : 27
