Systems of Equations Part I Assessment

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Systems of Equations (Part I)

Answer the question and solve the problems below. Make sure you show all your work so you can get partial credit even if you get the final answer wrong.

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $123.00 for 3 days and 300 miles, while Mary was charged $216.00 for 5 days and 600 miles. What does Best Rental charge per day, for mileage?

Let x = daily fee and y = mileage fee. The system of equations would then be as follows: Barney (3x + 300y = $123.00), Mary (5x + 600y = $216.00).

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We take Barney's equation and isolate for x:

300y = 123 (3x + 300y)/3 = 123/3 x + 100y = 41 x = 41-100y

Using substitution for Mary's equation, we get

5(41-100y) + 600y = 216-205 -- 500y + 600y = 216-205 + 100y = 216 100y = 11

Therefore, y = $0.11 per mileage

To find x, we plug into Barney's equation:

x = 41 -- 100y x = 41 -- 100(0.11) x = 41 -- 11 = $30.00 per day.

In conclusion, Best Rental charges $30.00 for a daily fee and $0.11 per mile.

2. There.....

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