Question 78611
Tropical pools sells an aboveground model for p dollars each. The monthly
revenue from the sale of this model is given by
R=-0.08pē + 300p
revenue is the product of the price p and the demand (quantity sold).
 
A) Factor out the price on the right hand side of the formula

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<pre><b>
R = -.08pē + 300p

Do what it says and factor out p

R = p(-.08p + 300)

</pre></b>
B) What is the expression of the monthly demand?
<pre><b>

We reason this way:

We first notice that it says

"revenue R is the product of the price p and the demand (quantity sold)."

We know that "product of p and the demand" means that p is multiplied by
demand.

Therefore we know that revenue R means "p multiplied by demand".

Now we look at the formula for the revenue R

R = p(-.08p + 300)

and ask ourselves "What is p multiplied by in that formula?"

We look and see that right after p we see a parentheses with 
(-.08p + 300).

So we say "Hey, in the formula for revenue R we see that
p is multiplied by (-.08p + 300)"

Then we look up there again where it says  

"revenue R means "p multiplied by demand".  

Then we reason "Well since the revenue R means "p multiplied by demand"
and we notice in the formula for revenue R has p next to and therefore
multiplied by (-.08p + 300), it must mean that the demand and (-.08p + 300)
are the same thing.  So since they are the same thing, they must be equal,
so we write

           DEMAND = -.08p + 300

</pre></b>
C) What is the monthly demand for the pool when the price is $3000
<pre><b>

Since p stands for price we plug in $3000 for p in the formula

           DEMAND = -.08p + 300
           DEMAND = -.08(3000) + 300
           DEMAND = -240 + 300
           DEMAND = 60

Since up there is says that the demand is the quantity sold, we
see that there must have been 60 sold.

Edwin</pre>