CPhill

Here's the graph...notice that everything that jboy314 has said is true !!

Actually, jboy314, you didn't leave much unsaid....the 'elimination" method is easy to use, but the "strategy" behind it is hard to explain  !!!

That's the question I thought you might ask !!!

We're trying to "match" terms so that, when we subtract one equation from the other, a variable "disappears."

Note that we could have mutiplied x + y = 1 by 6 on both sides giving 6x + 6y = 6

And, if  I  subtracted this from 5x + 6y = 6  notice that the "y's" would have disappeared, thusly

  5x + 6y = 6    ⇒    5x  + 6y  =  6

-[6x + 6y = 6]  ⇒   - 6x -  6y  = -6

----------------         ----------------

                              -1x         =   0            so ... x = 0  

And we could have found "y" by substituting 0 in for "x"  into the equation x + y = 1.....we would then find that y =1  ....just like before !!

This is an topic in Algebra (I don't know if you've encountered that or not)...so, if you haven't, don't worry about it too much....!!

Using what you've given me along with this formula (which I hope is the correct one!!), we have

P =  [(.07) (4148)] / [ 1 - (1 + .07)^-16] = $439.097  = $439.10

BTW.....It might be easiest to evaluate the numerator and denominator separately and then perform the division.....

Here's what jboy314 did, rosala

He took this equation ..... 9x + 9y = 9     and divided every term by 9.....so we have

9x/9  +  9y/9   = 9/9      and this gives us  

x + y  = 1       then, he multiplied every term by 5 ..(the reason for this will be clear in a second).. so we have

5x + 5y  = 1     Notice carefully, what happens if I take this equation and subtract it from  5x + 6y =6, we have:

         5x + 6y  = 6       ⇒    5x   + 6y  =  6   

-      (5x + 5y  = 5)      ⇒   -5x   -  5y  = -5

-----------------------           -----------------

                                                     y  =  1       

( Notice how the 5x terms cancelled each other !!!! That's why it's called the "elimination" method...jboy314  saw that he could eliminate  "x"  by multiplying x + y = 1 by 5 and then subtracting it from the other equation !!!! )

Now, all we need to do is to substitute  1 for y in any of the equations to find "x"...using x + y = 1 is easiest..so we have

x + (1) = 1      subtract 1 from both sides

   -   1  = -1

---------------

x         =   0

So  x = 0    and   y =1   are our solutions  !!!

density = mass / volume   ......so we have...

density = 5g / 10cm^3  =  .5g/cm^3

Makes perfect sense to me, rosala.....3 points and a "thumb"........!!!!

Nice explanation, jboy314.....3 points and a thumbs-up from me.....

BTW...welcome to the forum....I don't believe I've seen you here before.....

Well...if we started with 80 and had 3 left, we must have used 77.

So, 77/7 = 11 per day.....

On the first square we would have 2^0 = 1.

On the second square we would have 2^1 = 2

So, on the nth square, we would have  2^(n-1) grains.

So, on the 64th square, we would have 2^(64-1) = 2^(63) grains