Anna had 35 as many marbles as Penelope. The sum of the number of marbles Anna and Penelope had was the same as the number of marbles that Yen had. After trading, Yen gave 10% of her marbles to Anna and received 20% of Penelope's marbles. After that, Penelope 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 Anna's and Yen's marbles in the end.
| |
Anna |
Yen |
Penelope |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
3.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 1.2 u |
+ 1.2 u |
|
| After 2 |
10.8 u |
5.2 u |
16 u |
Total number of marbles that Anna and Penelope had at first
= 3 u + 5 u
= 8 u
Number of marbles that Yen had at first = 8 u
Number of marbles that Yen gave to Anna
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of marbles that Yen received from Penelope
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Penelope increased by when she continued to trade
= 30% x 4 u
=
30100 x 4 u
= 1.2 u
Number of marbles that Anna and Yen had in the end
= 3.8 u + 8.2 u - 1.2 u
= 10.8 u
In the end
Penelope : Anna and Yen
5.2 : 10.8
520 : 1080
13 : 27
Answer(s): 13 : 27
