Zara had 45 as many buttons as Rachel. The sum of the number of buttons Zara and Rachel had was the same as the number of buttons that Nicole had. After trading, Nicole gave 10% of her buttons to Zara and received 30% 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 Zara's and Nicole's buttons in the end.
| |
Zara |
Nicole |
Rachel |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 0.9 u |
- 0.9 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
4.9 u |
9.6 u |
3.5 u |
|
| Change 3 |
- 0.7 u |
+ 0.7 u |
|
| After 2 |
13.8 u |
4.2 u |
18 u |
Total number of buttons that Zara and Rachel had at first
= 4 u + 5 u
= 9 u
Number of buttons that Nicole had at first = 9 u
Number of buttons that Nicole gave to Zara
= 10% x 9 u
=
10100 x 4 u
= 0.9 u
Number of buttons that Nicole received from Rachel
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of buttons that Rachel increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of buttons that Zara and Nicole had in the end
= 4.9 u + 9.6 u - 0.7 u
= 13.8 u
In the end
Rachel : Zara and Nicole
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
