SOLUTION: A car rental compan has two rental rates. rate 1 is $72 per day plus $0.16 per mile. Rate 2 is $144 per day plus $0.08 per mile. If you plan to rent for one week, how many miles wo

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Question 151689: A car rental compan has two rental rates. rate 1 is $72 per day plus $0.16 per mile. Rate 2 is $144 per day plus $0.08 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 Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
First, we'll express the two rates as equations:
Rate 1 is $72 per day + $0.16 per mile.
Rate 2 is $144 per day + $0.08 per mile.
Since you are renting for one week (7 days) and letting x = the number of miles, we can refine the equations a bit:
=
=
Now the question is, what value of x (number of miles) will make , so we need to write the inequality:
Now we solve this inequality for x. Subtract 0.08x from both sides.
Now subtract 504 from both sides.
Finally, divide both sides by 0.08
or
So, you would need to drive more than 6300 miles to pay less with rate 2.
Let's check the answer by driving 6301 miles (6301 > 6300):

Rate 1 would be $1512.16 for one week's rental driven 6301 miles.

Rate 2 would be $1512.08 for one week's rental driven 6301 miles.
So you can see that if you were to drive more than 6300 miles for the week, rate 2 would cost you less than rate 1.