Hilda had 45 as many buttons as Ivory. The sum of the number of buttons Hilda and Ivory had was the same as the number of buttons that Irene had. After trading, Irene gave 10% of her buttons to Hilda and received 10% of Ivory's buttons. After that, Ivory 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 Hilda's and Irene's buttons in the end.
| |
Hilda |
Irene |
Ivory |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
4.9 u |
8.6 u |
4.5 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
12.6 u |
5.4 u |
18 u |
Total number of buttons that Hilda and Ivory had at first
= 4 u + 5 u
= 9 u
Number of buttons that Irene had at first = 9 u
Number of buttons that Irene gave to Hilda
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of buttons that Irene received from Ivory
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of buttons that Ivory increased by when she continued to trade
= 20% x 4.5 u
=
20100 x 4.5 u
= 0.9 u
Number of buttons that Hilda and Irene had in the end
= 4.9 u + 8.6 u - 0.9 u
= 12.6 u
In the end
Ivory : Hilda and Irene
5.4 : 12.6
540 : 1260
3 : 7
Answer(s): 3 : 7
