Opal had 45 as many buttons as Vanessa. The sum of the number of buttons Opal and Vanessa had was the same as the number of buttons that Kimberly had. After trading, Kimberly gave 30% of her buttons to Opal and received 40% of Vanessa's buttons. After that, Vanessa continued to trade and increased her number of buttons in the end by 10%, find the ratio of her number of buttons to the sum of Opal's and Kimberly's buttons in the end.
| |
Opal |
Kimberly |
Vanessa |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
6.7 u |
8.3 u |
3 u |
|
| Change 3 |
- 0.3 u |
+ 0.3 u |
|
| After 2 |
14.7 u |
3.3 u |
18 u |
Total number of buttons that Opal and Vanessa had at first
= 4 u + 5 u
= 9 u
Number of buttons that Kimberly had at first = 9 u
Number of buttons that Kimberly gave to Opal
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of buttons that Kimberly received from Vanessa
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of buttons that Vanessa increased by when she continued to trade
= 10% x 3 u
=
10100 x 3 u
= 0.3 u
Number of buttons that Opal and Kimberly had in the end
= 6.7 u + 8.3 u - 0.3 u
= 14.7 u
In the end
Vanessa : Opal and Kimberly
3.3 : 14.7
330 : 1470
11 : 49
Answer(s): 11 : 49
