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"Jonathan" <jp_wells@optusnet.com.au> wrote in message
news:3d1eedb4$0$25797$afc38c87@news.optusnet.com.au...
> As part of a school assignment I have to complete these two problems, but
I
> have no idea as to how to do them, I was wondering anyone knows how to do
> them?
>
> 1)  The product of two positive number is 12. Find the least value of
their
> sum. Is there a largest value?  (10 marks)

I seem to recall that the product of two numbers means 'multiply two numbers
together'.

Therefore 12 x 1 fits the bill as this equals 12.

So would 6 x 2 and 4 x3.

So the sum of 12 + 1 is 13, the sum of 6 and 2 is eight, so we have a
smaller sum and we are getting closer...the sum of 4 and 3 is 7, the
smallest so far!

Please note that 3.75 x 3.2 = 12 and this has a sum of 6.95 which is smaller
still.

Also, 3 1/3 (three and one-third) x 3.6 = 12 and sums to 6.93 (with the
three recurring), even smaller yet.

What about 3.409 (with the 0.409 part recurring) x 3.52?  This product
equals twelve and the sum is 6.92909 (the last two digits recurring) which
is even smaller still!

At this point I am getting bored of trying out numbers.  There is almost
certainly a technique for finding the least sum, but I do not know it, but I
have given you a start.

I don't believe that there is a 'largest number' since you could always make
one side double the size and compensate by making the other side half the
size

e.g. 12 x 1 = 12 (which sums to 13)

but then 24 x 0.5 = 12 and sums to 24.5
and then 48 x 0.25 = 12 and sums to 48.25 and so on and so on, until one
side is infinitely large and the other side is infinitely small.

If there is an answer it looks like infinitesimal calculus is involved, but
I don't know much about it!


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MESSAGE ENDS.
John Porcella