Gem had 45 as many buttons as Pamela. The sum of the number of buttons Gem and Pamela had was the same as the number of buttons that Yoko had. After trading, Yoko gave 30% of her buttons to Gem and received 20% of Pamela's buttons. After that, Pamela 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 Gem's and Yoko's buttons in the end.
| |
Gem |
Yoko |
Pamela |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1 u |
- 1 u |
|
| After 1 |
6.7 u |
7.3 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 Gem and Pamela had at first
= 4 u + 5 u
= 9 u
Number of buttons that Yoko had at first = 9 u
Number of buttons that Yoko gave to Gem
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of buttons that Yoko received from Pamela
= 20% x 5 u
=
20100 x 5 u
= 1 u
Number of buttons that Pamela increased by when she continued to trade
= 20% x 4 u
=
20100 x 4 u
= 0.8 u
Number of buttons that Gem and Yoko had in the end
= 6.7 u + 7.3 u - 0.8 u
= 13.2 u
In the end
Pamela : Gem and Yoko
4.8 : 13.2
480 : 1320
4 : 11
Answer(s): 4 : 11
