Linda had 45 as many buttons as Lynn. The sum of the number of buttons Linda and Lynn had was the same as the number of buttons that Diana had. After trading, Diana gave 20% of her buttons to Linda and received 20% of Lynn's buttons. After that, Lynn 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 Linda's and Diana's buttons in the end.
| |
Linda |
Diana |
Lynn |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
5.8 u |
8.2 u |
4 u |
|
| Change 3 |
- 0.8 u |
+ 0.8 u |
|
| After 2 |
13.2 u |
4.8 u |
18 u |
Total number of buttons that Linda and Lynn had at first
= 4 u + 5 u
= 9 u
Number of buttons that Diana had at first = 9 u
Number of buttons that Diana gave to Linda
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of buttons that Diana received from Lynn
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of buttons that Lynn increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of buttons that Linda and Diana had in the end
= 5.8 u + 8.2 u - 0.8 u
= 13.2 u
In the end
Lynn : Linda and Diana
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
