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