Shannon had 35 as many marbles as Betty. The sum of the number of marbles Shannon and Betty had was the same as the number of marbles that Kimberly had. After trading, Kimberly gave 20% of her marbles to Shannon and received 20% of Betty's marbles. After that, Betty 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 Shannon's and Kimberly's marbles in the end.
| |
Shannon |
Kimberly |
Betty |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 1.6 u |
- 1.6 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
4.6 u |
7.4 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 Shannon and Betty had at first
= 3 u + 5 u
= 8 u
Number of marbles that Kimberly had at first = 8 u
Number of marbles that Kimberly gave to Shannon
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of marbles that Kimberly received from Betty
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Betty increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of marbles that Shannon and Kimberly had in the end
= 4.6 u + 7.4 u - 0.8 u
= 11.2 u
In the end
Betty : Shannon and Kimberly
4.8 : 11.2
480 : 1120
3 : 7
Answer(s): 3 : 7
