Question 764073
Let {{{ x }}} = ounces of pure silver needed
{{{ 17.8x }}} = cost in dollars of pure silver 
{{{ 8.5*50 = 425 }}} = cost in dollars of 50 oz of silver alloy
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{{{ ( 17.8x + 425 ) / ( x + 50 ) = 15.3 }}}
{{{ 17.8x + 425 = 15.3*( x + 50 ) }}}
{{{ 17.8x + 425 = 15.3x + 765 }}}
{{{ 2.5x = 340 }}}
{{{ x = 136 }}}
136 ounces of pure silver are needed
check:
{{{ ( 17.8x + 425 ) / ( x + 50 ) = 15.3 }}}
{{{ ( 17.8*136 + 425 ) / ( 136 + 50 ) = 15.3 }}}
{{{  2845.8 / 186 = 15.3 }}}
{{{ 2845.8 = 15.3*186 }}}
{{{ 2845.8 = 2845.8 }}}
OK