Penelope had 35 as many marbles as Abi. The sum of the number of marbles Penelope and Abi had was the same as the number of marbles that Dana had. After trading, Dana gave 10% of her marbles to Penelope and received 20% of Abi's marbles. After that, Abi 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 Penelope's and Dana's marbles in the end.
| |
Penelope |
Dana |
Abi |
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 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
11.2 u |
4.8 u |
16 u |
Total number of marbles that Penelope and Abi had at first
= 3 u + 5 u
= 8 u
Number of marbles that Dana had at first = 8 u
Number of marbles that Dana gave to Penelope
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of marbles that Dana received from Abi
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Abi increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of marbles that Penelope and Dana had in the end
= 3.8 u + 8.2 u - 0.8 u
= 11.2 u
In the end
Abi : Penelope and Dana
4.8 : 11.2
480 : 1120
3 : 7
Answer(s): 3 : 7
