Jean had 45 as many buttons as Yoko. The sum of the number of buttons Jean and Yoko had was the same as the number of buttons that Barbara had. After trading, Barbara gave 10% of her buttons to Jean and received 40% of Yoko's buttons. After that, Yoko continued to trade and increased her number of buttons in the end by 20%, find the ratio of her number of buttons to the sum of Jean's and Barbara's buttons in the end.
| |
Jean |
Barbara |
Yoko |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
4.9 u |
10.1 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
14.4 u |
3.6 u |
18 u |
Total number of buttons that Jean and Yoko had at first
= 4 u + 5 u
= 9 u
Number of buttons that Barbara had at first = 9 u
Number of buttons that Barbara gave to Jean
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of buttons that Barbara received from Yoko
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of buttons that Yoko increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of buttons that Jean and Barbara had in the end
= 4.9 u + 10.1 u - 0.6 u
= 14.4 u
In the end
Yoko : Jean and Barbara
3.6 : 14.4
360 : 1440
1 : 4
Answer(s): 1 : 4
