Yoko had 45 as many marbles as Esther. The sum of the number of marbles Yoko and Esther had was the same as the number of marbles that Jaslyn had. After trading, Jaslyn gave 20% of her marbles to Yoko and received 30% of Esther's marbles. After that, Esther 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 Yoko's and Jaslyn's marbles in the end.
| |
Yoko |
Jaslyn |
Esther |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
5.8 u |
8.7 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of marbles that Yoko and Esther had at first
= 4 u + 5 u
= 9 u
Number of marbles that Jaslyn had at first = 9 u
Number of marbles that Jaslyn gave to Yoko
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of marbles that Jaslyn received from Esther
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of marbles that Esther increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of marbles that Yoko and Jaslyn had in the end
= 5.8 u + 8.7 u - 0.7 u
= 13.8 u
In the end
Esther : Yoko and Jaslyn
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
