SOLUTION: A car rental company has two rental rates. Rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day and $0.09 per mile. If you plan to rent for one week, how many miles w

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A car rental company has two rental rates. Rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day and $0.09 per mile. If you plan to rent for one week, how many miles w      Log On


   



Question 197730: A car rental company has two rental rates. Rate 1 is $35 per day plus $0.16 per mile. Rate 2 is $50 per day and $0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking rate 2?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let d= number of days rented
Let m= miles driven
given:
(1) 35d+%2B+.16m= rate 1
(2) 50d+%2B+.09m= rate 2
d+=+7
First find the break-even point by making rate 1 = rate 2
(1) 35d+%2B+.16m+=+50d+%2B+.09m
35%2A7+%2B+.16m+=+50%2A7+%2B+.09m
245+%2B+.16m+=+350+%2B+.09m
.07m+=+105
m+=+1500 mi
245+%2B+.16%2A1500+=+245+%2B+240
rate 1 = 485
350+%2B+.09%2A1500+=+350+%2B+135
rate 2 = 485
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If I drive 1 extra mile, which rate is lower?
(1) 35d+%2B+.16m= rate 1
245+%2B+.16%2A1501
245+%2B+240.16+=+485.16
and
(2) 50d+%2B+.09%2A1501= rate 2
350+%2B+135.09+=+485.09
Any milage over 1500 will make rate 2 less than rate 1
I'll plot the lines:
+graph%28+800%2C+500%2C+-300%2C+2000%2C+-30%2C+600%2C+245+%2B+.16x%2C+350+%2B+.09x%29+