Question 879352
Let {{{ n }}} = the number of muffins she started with
{{{ 4/n }}} = the cost per muffin
{{{ (4/n)*3 = 12/n }}} = the cost of 3 muffins
{{{ n - 3 }}} = the number of muffins she resold
{{{ ( 4 - 12/n )/( n-3 ) }}} = the cost per muffin that she resold
{{{ 3.5 / ( n - 3 ) }}} = her resale price per muffin
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She resold {{{ n-3 }}} muffins at {{{ .2 }}} dollars profit per muffin
I can say:
{{{ 3.5 / ( n-3 ) - ( 4 - 12/n ) / ( n-3 )  = .2 }}}
{{{ 3.5 - ( 4 - 12/n ) = .2*( n-3 ) }}}
{{{ 3.5 - 4 + 12/n = .2n - .6 }}}
{{{ -.5 + .6 = .2n - 12/n }}}
{{{ .1 = .2n - 12/n }}}
{{{ .1n = .2n^2 - 12 }}}
{{{ .2n^2 - .1n - 12 = 0 }}}
{{{ 2n^2 - n - 120 = 0 }}}
{{{ n = (-b +- sqrt( b^2 - 4*a*c ))/(2*a) }}}
{{{ n = (-(-1) +- sqrt( (-1)^2 - 4*2*(-120) ))/(2*2) }}}
{{{ n = ( 1 +- sqrt( 1 + 960 ))/ 4 }}}
{{{ n = ( 1 +- sqrt( 961 ))/ 4 }}}
{{{ n = ( 1 + 31 ) / 4 }}}
{{{ n = 32/4 }}}
{{{ n = 8 }}}
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she charged per muffin:
{{{ 3.5 / ( n - 3 ) }}}
{{{ 3.5 / ( 8 - 3 ) = 3.5/5 }}}
{{{ 3.5/5 = .7 }}}
70 cents per muffin
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check:
{{{ 8 }}} = the number of muffins she started with
{{{ 4/8 = .5 }}} = the cost per muffin
{{{ (4/8)*3 = 12/8 }}} = the cost of 3 muffins
{{{ 8 - 3 = 5 }}} = the number of muffins she resold
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{{{ ( 4 - 12/8 )/( 8-3 ) }}} = the cost per muffin that she resold
{{{ 2.5/5 = .5 }}} = the cost per muffin that she resold
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{{{ 3.5 / ( 8 - 3 ) }}} = her resale price per muffin
{{{ 3.5/5 = .7 }}} = her resale price per muffin
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Hope I got it!