Question 1045747
Let {{{ I }}} = income from sales of papers
{{{ I = ( 30000 - 2000x )*( 65 + .1x ) }}}
{{{ I = 2000*( 15 - x )*( 65 + .1x ) }}}
{{{ I = 2000*( 975 - 65x + 1.5x - .1x^2 ) }}}
{{{ 19350 = 2000*( 975 - 65x + 1.5x - .1x^2 ) }}}
{{{ 9.675 = 975 - 63.5x - .1x^2  }}}
{{{ -.1x^2 - 63.5x + 965.325 = 0 }}}
{{{ -x^2 - 635x + 9653.25 = 0 }}}
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Use quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = -1 }}}
{{{ b = -635 }}}
{{{ c = 9653.25 }}}
{{{ x = (-(-635) +- sqrt( (-635)^2-4*(-1)*9653.25 ))/(2*(-1)) }}} 
{{{ x = ( 635 +- sqrt( 403225 + 38613 ))/((-2)) }}} 
{{{ x = ( 635 +- sqrt( 441838 ))/((-2)) }}} 
{{{ x = ( 635 - 664.709 ) / (-2) }}}
{{{ x = ( -29.709 ) / (-2) }}}
{{{ x = 14.854 }}}
15 increases in price will give an income of $19,350
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check:
{{{ I = ( 30000 - 2000x )*( 65 + .1x ) }}}
{{{ I = ( 30000 - 2000*14.854 )*( 65 + .1*14.854 ) }}}
{{{ I = ( 30000 - 29708 )*( 65 + 1.4854 ) }}}
{{{ I = 292*66.4854 }}}
{{{ I = 19413.74 }}}
I'm a little off from actual income. I must have
a math error, but my method is good , I think