Question 844711
Let {{{ x }}} = the number of miles she
has to drive for the 2 plans to cost the same
Let {{{ C }}} = cost
For the 1st plan:
{{{ C = 55 + .5x }}}
For the 2nd plan:
{{{ C = .7x }}}
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Make the costs of the 2 plans the same
{{{ 55 + .5x = .7x }}}
{{{ .2x = 55 }}}
{{{ x = 275 }}}
Diane needs to drive 275 mi for the two plans to cost the same
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Here is the plot for the 2 plans:
{{{ graph( 600, 400, -50, 350, -50, 280, .5x + 55, .7x ) }}}