Question 549037
Find R when p = 100

Subsituting p=100 into R=p(200-p) we get:
{{{R=100(200-100)}}}
{{{R=100(100)}}}
{{{R=10000}}}




Find p when R = 7500
Substituting R=7500 into R=p(200-p) we get:
{{{7500=p(200-p)}}}
{{{7500=200p-p^2}}}
{{{p^2-200p-7500=0}}}
We can now use the quadratic formula which says 
{{{x=(-b+-sqrt(b^2-4ac))/2a}}}

And substituting our values in we get:
{{{p=(200+-sqrt(200^2-4*1*(-7500)))/2*1}}}
{{{p=(200+-sqrt(40000+30000))/2}}}
{{{p=(200+-sqrt(70000))/2}}}
{{{p=(200+-sqrt(4*17500))/2}}}
{{{p=(200+-sqrt(4)*sqrt(17500))/2}}}
{{{p=(200+-2*sqrt(17500))/2}}}
{{{p=(2(100+-sqrt(17500)))/2}}}
{{{p=(100+-sqrt(17500))}}}