Question 197730
Let {{{d}}}= number of days rented
Let {{{m}}}= miles driven
given:
(1) {{{35d + .16m}}}= rate 1
(2) {{{50d + .09m}}}= rate 2
{{{d = 7}}}
First find the break-even point by making rate 1 = rate 2
(1) {{{35d + .16m = 50d + .09m}}}
{{{35*7 + .16m = 50*7 + .09m}}}
{{{245 + .16m = 350 + .09m}}}
{{{.07m = 105}}}
{{{m = 1500}}} mi
{{{245 + .16*1500 = 245 + 240}}}
rate 1 = {{{485}}}
{{{350 + .09*1500 = 350 + 135}}}
rate 2 = {{{485}}}
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If I drive 1 extra mile, which rate is lower?
(1) {{{35d + .16m}}}= rate 1
{{{245 + .16*1501}}}
{{{245 + 240.16 = 485.16}}}
and
(2) {{{50d + .09*1501}}}= rate 2
{{{350 + 135.09 = 485.09}}}
Any milage over 1500 will make rate 2 less than rate 1
I'll plot the lines:
{{{ graph( 800, 500, -300, 2000, -30, 600, 245 + .16x, 350 + .09x) }}}