Ivory had 35 as many buttons as Jen. The sum of the number of buttons Ivory and Jen had was the same as the number of buttons that Nora had. After trading, Nora gave 10% of her buttons to Ivory and received 40% of Jen's buttons. After that, Jen 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 Ivory's and Nora's buttons in the end.
| |
Ivory |
Nora |
Jen |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
3.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of buttons that Ivory and Jen had at first
= 3 u + 5 u
= 8 u
Number of buttons that Nora had at first = 8 u
Number of buttons that Nora gave to Ivory
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of buttons that Nora received from Jen
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of buttons that Jen increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of buttons that Ivory and Nora had in the end
= 3.8 u + 9.2 u - 0.6 u
= 12.4 u
In the end
Jen : Ivory and Nora
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
