Question 536491
Let {{{ x }}} = pounds of Spanish peanuts she needs
given:
{{{ 3.5*10 = 35 }}} cost of Virginia peanuts used
{{{ 3x }}} = cost of Spanish peanuts used
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( cost of peanuts ) / ( weight in pounds ) = cost per pound of mixture
{{{ ( 35 + 3x ) / ( 10 + x ) = 3.4 }}}
{{{ 35 + 3x = 3.4*( 10 + x ) }}}
{{{ 35 + 3x = 34 + 3.4x }}}
{{{ .4x = 1 }}}
{{{ x = 2.5 }}}
She needs 2.5 pounds of spanish peanuts
check:
{{{ ( 35 + 3*2.5 ) / ( 10 + 2.5 ) = 3.4 }}}
{{{ ( 35 + 7.5 ) / 12.5 = 3.4 }}}
{{{ 42.5 / 12.5 = 3.4 }}}
{{{ 42.5 = 3.4*12.5 }}}
{{{ 42.5 = 42.5 }}}
OK