Usha had 45 as many marbles as Fiona. The sum of the number of marbles Usha and Fiona had was the same as the number of marbles that Tammy had. After trading, Tammy gave 10% of her marbles to Usha and received 30% of Fiona's marbles. After that, Fiona continued to trade and increased her number of marbles in the end by 20%, find the ratio of her number of marbles to the sum of Usha's and Tammy's marbles in the end.
| |
Usha |
Tammy |
Fiona |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
4.9 u |
9.6 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of marbles that Usha and Fiona had at first
= 4 u + 5 u
= 9 u
Number of marbles that Tammy had at first = 9 u
Number of marbles that Tammy gave to Usha
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of marbles that Tammy received from Fiona
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of marbles that Fiona increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of marbles that Usha and Tammy had in the end
= 4.9 u + 9.6 u - 0.7 u
= 13.8 u
In the end
Fiona : Usha and Tammy
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
