Lets set up some variables:
- 1st envelope: [tex]e_{1}[/tex]
- 2nd envelope: [tex]e_{2}[/tex]
- 3rd envelope: [tex]e_{3}[/tex]
Now let us set up some equations based of the facts:
- [tex]e_{1} +2=\frac{e_{2} }{2} -- > e_{2} = 2e_{1} +4[/tex]
- [tex]2e_{3} =e_{1} +e_{2}[/tex]
- [tex]e_{2} > e_{3} > e_{1}[/tex]
Now we could try some numbers out since there isn't really any other way I could solve this so far...
but we do know that the sum of [tex]e_{1}[/tex] and [tex]e_{2}[/tex] must be even since they equal [tex]2e_{3}[/tex]
After you tried it out for a little bit, when [tex]e_{1}[/tex] = 2, then [tex]e_{2}[/tex] = 8, and [tex]e_{3} = 5[/tex]. These three values meet the criteria and we have our answer.
Hope that helped!
