Nicole had 45 as many marbles as Diana. The sum of the number of marbles Nicole and Diana had was the same as the number of marbles that Shannon had. After trading, Shannon gave 30% of her marbles to Nicole and received 40% of Diana's marbles. After that, Diana 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 Nicole's and Shannon's marbles in the end.
| |
Nicole |
Shannon |
Diana |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of marbles that Nicole and Diana had at first
= 4 u + 5 u
= 9 u
Number of marbles that Shannon had at first = 9 u
Number of marbles that Shannon gave to Nicole
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of marbles that Shannon received from Diana
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of marbles that Diana increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of marbles that Nicole and Shannon had in the end
= 6.7 u + 8.3 u - 0.6 u
= 14.4 u
In the end
Diana : Nicole and Shannon
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
