Melody

Ok KidDanger BUT

if you use order of operation correctly  (that's  PEDMAS)  then

303.92*10^9 /11.2*10^6

actually means

$${\frac{{\mathtt{303.92}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{9}}}}{{\mathtt{11.2}}}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{6}}} = {\mathtt{27\,135\,714\,285\,714\,285.714\: \!285\: \!714\: \!285\: \!714\: \!3}}$$

Good thinking KidDanger :)

Thanks for that great answer Heureka :)

That is a really good answer Mellie :))

The other way is to solve the diophantine equation more formally.

I have done the first one on a peice of paper in front of me but it takes even longer to get to your answer than the easier way that I just used, so do it the easy way :))

Hi Mellie,

Now, we can do this the easy way .... or we can do it the hard way.

I'll start with the easy way

11x+8y=96

if x=0     8y=96    y=12          So   12 * 8 confusion notes will be good

if x=1    

11+8y=96

8y=85     No integer solution

if x=2          22+8y=96        8y=74        No integer solution

if x=3           33+8y=96        no integer solution

Just keep doing this and you will find that the only other solution is     

8*11confusions+1*8confusion      88+8=96

So there are only 2 ways.

You can do the other two similarly. :)    

This method is time consuming but the numbers are all quite small so it is quite doable :)

Well aren't you just so clever.  I worked it out Too :))

Thanks Chris,

I had very good maths teachers when I was at school (most of the time).  I am very grateful to them because these formative years are very important to learn the concepts and also for teaching the concepts at a later time.

This building up of graphs was not taught to me at school, perhaps the rudiments of it were but I mostly worked it out for myself.  It is an incredibly useful concept to understand. And it is fun seeing the graphs 'grow' from the germ of a beginning.

Desmos graphing calculator is a fantastic tool to show how the procedure works :)

No.. Heureka and I have got that one nailed!

You should try learning Latex.  It is like everything, the more you know the easier it is to add to your knowledge.  

Getting started is the hardest bit but then it becomes easy.  And you can start with really trivial things here so even getting started is not so hard. :)

It is much easier to makes sense of well presented material - and that usually means LaTex.