Betty had 45 as many pens as Opal. The sum of the number of pens Betty and Opal had was the same as the number of pens that Ivory had. After trading, Ivory gave 30% of her pens to Betty 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 Betty's and Ivory's pens in the end.
| |
Betty |
Ivory |
Opal |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 1.25 u |
- 1.25 u |
|
| After 1 |
6.7 u |
7.55 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 Betty and Opal had at first
= 4 u + 5 u
= 9 u
Number of pens that Ivory had at first = 9 u
Number of pens that Ivory gave to Betty
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of pens that Ivory 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 Betty and Ivory had in the end
= 6.7 u + 7.55 u - 0.75 u
= 13.5 u
In the end
Opal : Betty and Ivory
4.5 : 13.5
450 : 1350
1 : 3
Answer(s): 1 : 3
