Marion had 35 as many pens as Julie. The sum of the number of pens Marion and Julie had was the same as the number of pens that Tammy had. After trading, Tammy gave 10% of her pens to Marion and received 40% of Julie's pens. After that, Julie 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 Marion's and Tammy's pens in the end.
| |
Marion |
Tammy |
Julie |
Total |
| Before |
3 u |
8 u |
5 u |
16 u |
| Change 1 |
+ 0.8 u |
- 0.8 u |
|
|
| Change 2 |
|
+ 2 u |
- 2 u |
|
| After 1 |
3.8 u |
9.2 u |
3 u |
|
| Change 3 |
- 0.6 u |
+ 0.6 u |
|
| After 2 |
12.4 u |
3.6 u |
16 u |
Total number of pens that Marion and Julie had at first
= 3 u + 5 u
= 8 u
Number of pens that Tammy had at first = 8 u
Number of pens that Tammy gave to Marion
= 10% x 8 u
=
10100 x 3 u
= 0.8 u
Number of pens that Tammy received from Julie
= 40% x 5 u
=
40100 x 5 u
= 2 u
Number of pens that Julie increased by when she continued to trade
= 20% x 3 u
=
20100 x 3 u
= 0.6 u
Number of pens that Marion and Tammy had in the end
= 3.8 u + 9.2 u - 0.6 u
= 12.4 u
In the end
Julie : Marion and Tammy
3.6 : 12.4
360 : 1240
9 : 31
Answer(s): 9 : 31
