Barbara had 35 as many marbles as Roshel. The sum of the number of marbles Barbara and Roshel had was the same as the number of marbles that Emily had. After trading, Emily gave 10% of her marbles to Barbara and received 25% of Roshel's marbles. After that, Roshel 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 Barbara's and Emily's marbles in the end.
| |
Barbara |
Emily |
Roshel |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
3.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of marbles that Barbara and Roshel had at first
= 3 u + 5 u
= 8 u
Number of marbles that Emily had at first = 8 u
Number of marbles that Emily gave to Barbara
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of marbles that Emily received from Roshel
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of marbles that Roshel increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of marbles that Barbara and Emily had in the end
= 3.8 u + 8.45 u - 0.75 u
= 11.5 u
In the end
Roshel : Barbara and Emily
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
