Question 201512
a)
{{{250 + 10x}}}
b)
{{{(70 - 2x)(250 + 10x)}}}
c)
{{{17980 = (70 - 2x)(250 + 10x)}}}
{{{17980 = 17500 - 500x + 700x - 20x^2}}}
{{{-20x^2 + 200x - 480 = 0}}}
{{{-x^2 + 10x - 24 = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -1}}}
{{{b = 10}}}
{{{c = -24}}}
{{{x = (-10 +- sqrt( 10^2-4*(-1)*(-24) ))/(2*(-1)) }}}
{{{x = (-10 +- sqrt( 100 - 96 ))/(-2) }}}
{{{x = (-10 +- sqrt( 4 ))/(-2) }}}
{{{x = (5 -1 )}}}
{{{x = 4}}}
{{{x = (5 + 1)}}}
{{{x = 6}}}
He can make either 4 or 6 $10 rent increases
check:
{{{17980 = (70 - 2x)(250 + 10x)}}}
{{{17980 = (70 - 2*4)(250 + 10*4)}}}
{{{17980 = (62)(290)}}}
{{{17980 = 17980}}}
and
{{{17980 = (70 - 2x)(250 + 10x)}}}
{{{17980 = (70 - 2*6)(250 + 10*6)}}}
{{{17980 = (58)(310)}}}
{{{17980 = 17980}}}