Elyse had 45 as many pens as Olivia. The sum of the number of pens Elyse and Olivia had was the same as the number of pens that Jade had. After trading, Jade gave 20% of her pens to Elyse and received 30% of Olivia's pens. After that, Olivia 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 Elyse's and Jade's pens in the end.
| |
Elyse |
Jade |
Olivia |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 1.8 u |
- 1.8 u |
|
|
| Change 2 |
|
+ 1.5 u |
- 1.5 u |
|
| After 1 |
5.8 u |
8.7 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 pens that Elyse and Olivia had at first
= 4 u + 5 u
= 9 u
Number of pens that Jade had at first = 9 u
Number of pens that Jade gave to Elyse
= 20% x 9 u
=
20100 x 4 u
= 1.8 u
Number of pens that Jade received from Olivia
= 30% x 5 u
=
30100 x 5 u
= 1.5 u
Number of pens that Olivia increased by when she continued to trade
= 20% x 3.5 u
=
20100 x 3.5 u
= 0.7 u
Number of pens that Elyse and Jade had in the end
= 5.8 u + 8.7 u - 0.7 u
= 13.8 u
In the end
Olivia : Elyse and Jade
4.2 : 13.8
420 : 1380
7 : 23
Answer(s): 7 : 23
