Question 1051992
First I would find the number of miles
driven which makes the cost of the 2 plans equal
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You are renting for 1 day
Let {{{ n }}} = the number of miles driven
{{{ 32*1 + .09n = 18*1 + .12n }}}
{{{ .03n = 32 - 18 }}}
{{{ .03n = 14 }}}
{{{ n = 466.667 }}}
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I'll reduce the number of miles driven and
see if the B car costs less than the A car
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{{{ n = 466 }}}
A car:
{{{ 32*1 + .09*466 = 32 + 41.94 }}}
{{{ 32 + 41.94 = 73.94 }}}
B car:
{{{ 18*1 + .12*466 = 18 + 55.92 }}}
{{{ 18 + 55.92 = 73.92 }}}
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Car B costs less, so the most miles you can
drive so that a B car costs less than an A car is 466 mi
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Here's a plot of the 2 plans for 1 day:
{{{ graph( 500, 500, -60, 600, -10, 110, 32 + .09x, 18 + .12x ) }}}