Math Is Fun Forum

Hi nimsun!

Let C=Cost,    M=Margin,    DC=Dealer Commission,    SC=Salesman Commission,    T=Tax.
From your simple math calculation of 116.5 I see that you are calculating the DC, SC and T on
the total C+M, which we can call A; that is, let A=C+M=100.

Let R be the Dealer Commission RATE (which is given as 10%).

Your "working backwards" appears to involve only the DC and the total 116.5 and LEAVES OUT
the SC and the T.

The complete equation from your simple math is

                  (C+M) +  SC  +  DC  +   T    = total = 116.5  which is
                      A    + .02A + .10A +.045A = A+.165A = 1.165A = 1.165*100 = 116.5 

Then working backwards (solving for R given the total 116.5) replacing DC by R*A we obtain

       A  +   .02A    + R*A +    .045A
= 100 + .02(100) + R*A + .045(100)
= R*A+106.5

But this R*A+106.5 is the total 116.5; that is, R*A+106.5=116.5  so  R*A = 10.

Thus R*A = R*100 = 10  yields  R=10/100 = .10 = 10%

( .10A = 10 yields A = 100 which checks.)

This is one advantage of using algebra.  Give the unknown a name (here R) and write the equation
from the "simple math" approach.  Then solve for the unknown.  This allows us to get the
necessary equation reasoning from our "simple math" approach.

Have a very blessed day and New Year! 

Hi pellerinb!

I don't understand what you mean y "each with unique factors" for the consecutive numbers
(necessarily odd since if even they would have 2 in common).  Any two consecutive odd integers
must have no factors in common other than 1 since the difference of the two (larger less smaller)
is 2.  This means the only possible common factors are 2 and 1 and certainly 2 is not a common
factor for these odd integers.

Please clarify.

Hi digits!

Math is not so much a matter of grey matter as it is a question of language --- symbolism,
definitions, algorithms, notation, etc.  It was created over a period of thousands of years by folks
that couldn't communicate together (like we are blessed to be able to do in this present age) and
so we have a hodgepodge of language which is often redundant, misleading, cumbersome, harder
to manipulate than necessary and at times just plain wrong.  Not to mention that mathematicians
often disagree on notation, definitions, concepts etc.

Most folks are led to believe that math is as near perfect as anything that mankind has created.
Consequently they usually blame themselves ultimately when they have trouble with math.
Unlike the sciences where theories come and go math is based on logic, definitions, axioms,
theorems, algorithms, etc.  So what could possibly go wrong?  Hint:  It was created by human
beings.   

Since you and your husband both are interested in math you might google "math the original four
letter word" and enjoy some of the sites that pop up.  Some of the sites point out some of the
problems with the language of mathematics.

But of course it doesn't hurt to have great intellect, a photographic memory, lots of creativity, etc.
for doing mathematics.  It is just that most of us are not "giants" like Gauss, Euler, von Neuman,
etc.''  I've always had to work hard to understand mathematics (at least the small part of it that
I know).

Have a very blessed year this year! 

Not quite as accurate but easy to remember:  Studder quoting the first three odd positive integers
1 1 3 3 5 5 and divide the 113 into the 355 to get 3.141593 accurate to 7 significant figures.

                    3. 1 4 1 5 9 2 9 ...
             ____________________  rounds to 3.141593  same as 3.14159265... does.
    1 1 3 | 3 5 5. 0 0 0 0 0 0 0 0 0

julianthemath,  Have you see the fact that

  logy       logx
x        = y         which is still true for any positive base b (not 1) and positive x and y? 

One might get some interesting variations on these log problems using this fact.

1997-197 = 1000

Oops!  Off to a great start for the new year I am!

Should have been 1997-997.

((9)(.11111111...))^2=.999999999...

When Al Gore goes jogging his pace is called an algorithm.  And if he runs across fallen tree trunks
then it is also a ...  But it is difficult for him if the logs don't line up nicely.  So maybe an algorithm
can be a missfelled logarithm, eh mikau?

One approach:  Work out lots of cases and examples and look for patterns that can be turned into
formulas.  Nowadays it is lots easier to do with the aid of computers that can run out cases by the
bucket load. 

Anybody else care to contribute your favorite methods?

I'm getting the same as bobbym.  It sometimes helps to write the original function in terms of
a different variable than the one you are substituting in its place.  For example

f(x) = x^3+6x^2+12x+8 = x^3 + 2*3x^2 + 4*3x + 8 = (x+2)^3

f(x) = (x+2)^3 so f(t-1) = ((t-1)+2)^3 = (t+1)^3 = t^3+3t^2+3t+1 = (1, 3, 3, 1) by replacing
x by t-1 in the f(x) = (x+2)^3.

And as another example find the quadruple for f(t-2).

f(x) = (x+2)^3 so f(t-2) = ((t-2)+2)^3 = t^3 = (3, 0, 0, 0). 

These can also be looked at as a composition of functions: f(x)=(x+2)^3 and g(x)=x-1.

(fog)(x) = f(g(x)) = f(x-1) = ( (x-1)+2)^3 = (x+1)^3 

Of course this is all assuming that the guys aren't freaked out and can figure out what's going on.
The back guy and middle guy might be unable to think under the pressure and so just say "I don't
know".  But then at least one of them must guess, so they have at least a 50/50 chance!   I'm
not sure I could think under those circumstances!

I googled "scienceisfun.com and got no hits.  I did get a hit on "scienceisfun.org for a 7th grade
teacher Linda Smith.  On Yahoo I got a hit on "scienceisfun.com" but it just opened up a page of
ads.  So might "scienceisfunforum.com still be a possibility?