Penelope had 45 as many marbles as Lucy. The sum of the number of marbles Penelope and Lucy had was the same as the number of marbles that Barbara had. After trading, Barbara gave 10% of her marbles to Penelope and received 20% of Lucy's marbles. After that, Lucy 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 Barbara's marbles in the end.
| |
Penelope |
Barbara |
Lucy |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.9 u |
9.1 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of marbles that Penelope and Lucy had at first
= 4 u + 5 u
= 9 u
Number of marbles that Barbara had at first = 9 u
Number of marbles that Barbara gave to Penelope
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of marbles that Barbara received from Lucy
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Lucy increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of marbles that Penelope and Barbara had in the end
= 4.9 u + 9.1 u - 0.8 u
= 13.2 u
In the end
Lucy : Penelope and Barbara
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
