<PRE><B>Question 778224</B>
Let {{{ x }}} = number of miles driven in the city
{{{ 447 - x }}} = miles driven on highway
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Note that:
( miles driven ) / ( miles / gallon  ) = ( gallons used )
I can say:
{{{ x / 49 + ( 447 - x ) / 51  = 9 }}}
Multiply both sides by {{{ 49*51 }}}
{{{ 51x + 49*( 447 - x ) = 9*49*51 }}}
{{{ 51x + 21903 - 49x = 22491 }}}
{{{ 2x = 22491 - 21903 }}}
{{{ 2x = 588 }}}
{{{ x = 294 }}}
{{{ 447 - 294 = 153 }}}
294 miles were driven in the city
153 miles were driven on highway
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check:
{{{ x / 49 + ( 447 - x ) / 51  = 9 }}}
{{{ 294 / 49 + 153 / 51  = 9 }}}
{{{  6 + 3 = 9 }}}
{{{ 9 = 9 }}}
OK</PRE>