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