Can you cut a cake fairly to solve this middle school math problem?

[Whateverist]

How about I just give everyone icing-less cake and I keep the icing all to myself?

I do make a pretty badass icing, if I do say so myself. Many of my fellow students in school begged me to make their graduation cakes for them.

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And therein lies the solution:

You scrape all of the icing off the cake first, then cut the cake into five equal portions. Then you take the icing and divide it into five equal portions and let everyone put their share of icing on their share of cake.


/thread.

Now you're thinking like the students I used to have, whose street smarts inclined them to choose the practical over the idealized hypothetical.  Every year at least one student would suggest putting the whole cake, frosting and all, in a blender and serving it like a pudding equally.

[Joods]

Well this would be the sensible thing to do if you were on a liquid diet

[Chad32]

Only if the icing is spread unevenly. Is that part of the problem? If she did spread it unevenly, and everyone's going to bicker about wanting exactly the same amount of cake and icing, then just spread it evenly then cut. Or tell people to not be petty.

It is that attitude which makes pitching a math problem so hard.  

Have I mentioned I hate math? Could you say I'm trying to....cut corners, with this problem?

[Whateverist]

It is that attitude which makes pitching a math problem so hard.  

Have I mentioned I hate math?  Could you say I'm trying to....cut corners, with this problem?

Cutting corners .. C-!

[Joods]

Hey Chad - be happy you at least got a grade.

I didn't get one.

[Whateverist]

Umm .. that doesn't mean your score will be C(C – 1)(C – 2)(C – 3) ...

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Hey Chad - be happy you at least got a grade.

I didn't get one.

C- with a happy face for creativity.  Happy now?

[Joods]

No because it took six pages for someone to finally think outside of the box... the bell curve should have been nicer to me than a C-

[Whateverist]

Ok, how about an A+ for your curves then? (But you'll have to cum see me after class.)

[Joods]

Ok, how about an A+ for your curves then?  (But you'll have to cum see me after class.)

LMAO.... that'll cost you extra.

[popeyespappy]

How about I just give everyone icing-less cake and I keep the icing all to myself?

I do make a pretty badass icing, if I do say so myself. Many of my fellow students in school begged me to make their graduation cakes for them.

---

And therein lies the solution:

You scrape all of the icing off the cake first, then cut the cake into five equal portions. Then you take the icing and divide it into five equal portions and let everyone put their share of icing on their share of cake.


/thread.

I know what he was trying to say, but he is trying to make the problem harder than warranted for a middle school math question. The intent of the problem was to solve for volume (cake) and surface area (icing). It gets a lot more complicated if you want to solve for the volume of the cake and the volume of the icing. Let's say we have a 20x20x5 cake covered top and sides with 0.5 cm of icing.

Cake volume: 20x20x5=20003cm
Cake each: 2000/5=4003cm

Icing volume: (21x21x5.5)-(20x20x5)=425.53cm
Icing each: 425.5/5=105.13cm

That sounds easy enough. Just cut it up so that everyone gets 4003cm of cake and 105.13cm of icing. The problem is if you solve for icing volume the cake is off. If you solve for cake the icing is off because of the 4 corners. Each corner has 1.3753cm of icing and you can't divide those 4 corners 5 ways without separating them from everything else first.

ETA: In the solution I posted on page 3 a 20x20 cake with a 1/2 cm of icing on the top and sides everyone would have received 4003cm of cake, but 3 of the pieces would have had 85.3753cm of icing and the other two would have had 84.68753cm of icing. There is no simple solution for the volume plus volume problem of this sort when the number of pieces isn't a multiple of the corners.