SOLUTION: I have literally spent an entire day on this question. I think that it must be an inequality and some division must take place, but I am unable to find the solution. Here is the qu

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Question 241178: I have literally spent an entire day on this question. I think that it must be an inequality and some division must take place, but I am unable to find the solution. Here is the question:
A car rental company has two rental rates. Rate 1 is $63 per day plus .18 per mile. Rate 2 is $126 per day and .09 per mile. If you plan to rent a car for one week, how many miles would you need to drive to pay less by taking rate 2?
Any help is greatly appreciated.
Found 2 solutions by scott8148, kensson:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
7 days in a week
set the two costs equal to find the "break even" milage

7(63) + .18m = 7(126) + .09m

subtracting [.09m + 7(63)] ___ .09m = 7(63)

dividing by .09 ___ m = 7(700) = 4900 miles

you need to drive MORE THAN this to save money with rate 2

Answer by kensson(21) About Me  (Show Source):
You can put this solution on YOUR website!
For rate 1, you pay +R1+=%2863+%2A+7%29+%2B+0.18m
For rate 2, you pay +R2+=+%28126+%2A+7%29+%2B+0.09m
For R2 < R1, you have +882+%2B+0.09m+%3C+441+%2B+0.18m+
Subtract 441+%2B+0.09m from each side to leave +441+%3C+0.09m+
Divide by 0.09 to give 4900+%3C+m
m is then at least 4900 miles! 700 miles a day is a lot of driving.