Question #4669

5. Suppose one car rental company charges $15 per day plus $0.20 per mile while a second one charges $25 per day plus $0.15 per mile. Answer each of the following questions assuming you only plan on renting the car for one day:
a) Give an expression for the total cost of driving x miles if we rent from the first agency.
b) Give an expression for the total cost of driving x miles if we rent from the second agency.
c) If we’re only going to drive 100 miles, which agency should we choose?
d) For what distance will the two agencies charge the same amount?

Expert's answer

1) charges $15 per day plus $0.20 per mile

2) charges $25 per day plus $0.15 per mile

a) if we rent from the first agency, then its TC1 = 15 + 0.2*S, where S - distance in miles.

b) If we rent from the second agency, then its TC2 = 25 + 0.15*S.

c) If we’re only going to drive 100 miles, then TC1 = 15 + 0.2*100 = 35,

TC2 = 25 + 0.15*100 = 40, so which we should choose first agency.

d) The two agencies will charge the same amount, when TC1 = TC2, so:

15 + 0.2S = 25 + 0.15S

0.05S = 10

S = 200 miles.

2) charges $25 per day plus $0.15 per mile

a) if we rent from the first agency, then its TC1 = 15 + 0.2*S, where S - distance in miles.

b) If we rent from the second agency, then its TC2 = 25 + 0.15*S.

c) If we’re only going to drive 100 miles, then TC1 = 15 + 0.2*100 = 35,

TC2 = 25 + 0.15*100 = 40, so which we should choose first agency.

d) The two agencies will charge the same amount, when TC1 = TC2, so:

15 + 0.2S = 25 + 0.15S

0.05S = 10

S = 200 miles.

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