Risa had 45 as many marbles as Linda. The sum of the number of marbles Risa and Linda had was the same as the number of marbles that Lynn had. After trading, Lynn gave 10% of her marbles to Risa and received 25% of Linda's marbles. After that, Linda 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 Risa's and Lynn's marbles in the end.
| |
Risa |
Lynn |
Linda |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
4.9 u |
9.35 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of marbles that Risa and Linda had at first
= 4 u + 5 u
= 9 u
Number of marbles that Lynn had at first = 9 u
Number of marbles that Lynn gave to Risa
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of marbles that Lynn received from Linda
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of marbles that Linda increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of marbles that Risa and Lynn had in the end
= 4.9 u + 9.35 u - 0.75 u
= 13.5 u
In the end
Linda : Risa and Lynn
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
