SOLUTION: Please help with the following word problem? Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $69 for 3 days and 300 miles, while Mary

Question 450034: Please help with the following word problem?
Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $69 for 3 days and 300 miles, while Mary was charged $123 for 5 days and 600 miles. Find the daily fee and find the mileage charge?
I have no idea where to start! Thanks!
Found 2 solutions by htmentor, solver91311:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let d = the daily fee
Let m = the mileage charge
For Barney's charges we can write:
69 = 3d + 300m [3 day rental, 300 mi]
For Mary's charges, we can write:
123 = 5d + 600m [ 5 day rental, 600 mi]
We have two equations and two unknowns so we can solve.
Multiplying the 1st equation by 2 and subtracting the 2nd gives:
138 - 123 = 6d - 5d
15 = d
Now we can use this value for d to solve for m. From the 1st equation above, we have:
69 = 3(15) + 300m
24/300 = m = 0.08
Therefore, the daily fee is $15 and the mileage charge is $0.08 per mile.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let represent the amount charged per mile. Let represent the daily fee.

In the first situation, where the mileage fee represents the cost of traveling 300 miles, that cost can be expressed as . That is, the number of miles traveled times the cost per mile. Furthermore, the cost for the daily fee for the 3 days is represented by , i.e. the number of days times the daily fee. The sum of the two is given as $69, hence:

In a similar fashion, we can derive another equation that describes the second situation:

Now all you have to do is solve the system for the ordered pair . Hint: Since the larger coefficient on is an integer multiple of the other, this system lends itself nicely to the Elimination method. Just multiply the first equation by -2 and proceed.

John

My calculator said it, I believe it, that settles it

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