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