Wendy had 45 as many pens as Opal. The sum of the number of pens Wendy and Opal had was the same as the number of pens that Diana had. After trading, Diana gave 20% of her pens to Wendy and received 25% of Opal's pens. After that, Opal continued to trade and increased her number of pens in the end by 20%, find the ratio of her number of pens to the sum of Wendy's and Diana's pens in the end.
| |
Wendy |
Diana |
Opal |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
5.8 u |
8.45 u |
3.75 u |
|
| Change 3 |
- 0.75 u |
+ 0.75 u |
|
| After 2 |
13.5 u |
4.5 u |
18 u |
Total number of pens that Wendy and Opal had at first
= 4 u + 5 u
= 9 u
Number of pens that Diana had at first = 9 u
Number of pens that Diana gave to Wendy
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of pens that Diana received from Opal
= 25% x 5 u
=
25100 x 5 u
= 1.25 u
Number of pens that Opal increased by when she continued to trade
= 20% x 3.75 u
=
20100 x 3.75 u
= 0.75 u
Number of pens that Wendy and Diana had in the end
= 5.8 u + 8.45 u - 0.75 u
= 13.5 u
In the end
Opal : Wendy and Diana
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
