Wendy had 35 as many marbles as Diana. The sum of the number of marbles Wendy and Diana had was the same as the number of marbles that Joelle had. After trading, Joelle gave 20% of her marbles to Wendy and received 20% of Diana's marbles. After that, Diana continued to trade and increased her number of marbles in the end by 10%, find the ratio of her number of marbles to the sum of Wendy's and Joelle's marbles in the end.
| |
Wendy |
Joelle |
Diana |
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 |
- 0.4 u |
+ 0.4 u |
|
| After 2 |
11.6 u |
4.4 u |
16 u |
Total number of marbles that Wendy and Diana had at first
= 3 u + 5 u
= 8 u
Number of marbles that Joelle had at first = 8 u
Number of marbles that Joelle gave to Wendy
= 20% x 8 u
=
20100 x 3 u
= 1.6 u
Number of marbles that Joelle received from Diana
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of marbles that Diana increased by when she continued to trade
= 10% x 4 u
=
10100 x 4 u
= 0.4 u
Number of marbles that Wendy and Joelle had in the end
= 4.6 u + 7.4 u - 0.4 u
= 11.6 u
In the end
Diana : Wendy and Joelle
4.4 : 11.6
440 : 1160
11 : 29
Answer(s): 11 : 29
