Question 1053917
Let {{{ x }}} = pounds of the $6 coffee needed
{{{ 15*30 = 450 }}} = cost of 30 pounds of $15 used
{{{ 6x }}} = cost of the $6 coffee used
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{{{ ( 6x + 450 ) / ( x + 30 ) = 12 }}}
( this is [ cost/lb ] = [ cost/lb ] )
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{{{ 6x + 450 = 12*( x + 30 ) }}}
{{{ 6x + 450 = 12x + 360 }}}
{{{ 6x = 90 }}}
{{{ x = 15 }}}
15 pounds of the $6 coffee are needed
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check:
{{{ ( 6x + 450 ) / ( x + 30 ) = 12 }}}
{{{ ( 6*15 + 450 ) / ( 15 + 30 ) = 12 }}}
{{{ ( 90 + 450 ) / 45 = 12 }}}
{{{ 540 / 45 = 12 }}}
{{{ 540 = 540 }}}
OK