Question 1082652
Let {{{ x }}} = the number of gallons in a full tank
The fuel efficiency is:
{{{ 315 / ( x-9 ) }}}
and, also:
{{{ 240 / ( x - 14 ) }}}
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The fuel efficiency doesn't change, so:
{{{ 315 / ( x - 9 ) = 240 / ( x - 14 ) }}}
Multiply both sides by {{{ ( x - 9 )*( x - 14 ) }}}
{{{ 315*( x - 14 ) = 240*( x - 9 ) }}}
{{{ 21*( x - 14 ) = 16*( x - 9 ) }}}
{{{ 21x - 294 = 16x - 144 }}}
{{{ 5x = 150 }}}
{{{ x = 30 }}}
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The fuel efficiency is:
{{{ 315 / ( x - 9 ) }}}
{{{ 315 / ( 30 - 9 ) }}}
{{{ 315 / 21 = 15 }}}
15 miles/gallon
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The miles you could drive on a full tank:
{{{ 15x = 15*30 }}}
{{{ 15x = 450 }}}
450 miles
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check:
{{{ 240 / ( x - 14 ) }}}
{{{ 240 / ( 30 - 14 ) }}}
{{{ 240 / 16 = 15 }}}
15 miles/gallon
OK