# Answer to Question #4669 in Algebra for merveille

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&rsquo;re only going to drive 100 miles, which agency should we choose? d) For what distance will the two agencies charge the same amount?
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.

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