Yoko had 35 as many buttons as Nicole. The sum of the number of buttons Yoko and Nicole had was the same as the number of buttons that Mary had. After trading, Mary gave 10% of her buttons to Yoko and received 25% of Nicole's buttons. After that, Nicole 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 Yoko's and Mary's buttons in the end.
| |
Yoko |
Mary |
Nicole |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
3.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
11.5 u |
4.5 u |
16 u |
Total number of buttons that Yoko and Nicole had at first
= 3 u + 5 u
= 8 u
Number of buttons that Mary had at first = 8 u
Number of buttons that Mary gave to Yoko
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of buttons that Mary received from Nicole
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of buttons that Nicole increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of buttons that Yoko and Mary had in the end
= 3.8 u + 8.45 u - 0.75 u
= 11.5 u
In the end
Nicole : Yoko and Mary
4.5 : 11.5
450 : 1150
9 : 23
Answer(s): 9 : 23
