Suppose that a car rental agency charges a fixed amount per day plus an amount per mile for renting a car. Heidi rented a car one day and paid $100.00 for 300 miles. On another day she rented a car from the same agency and paid $150.00 for 550 miles. Determine the linear function that the agency could use to determine its daily rental charges.
A)f ( x )= 0.4 x - 40
B)f ( x )= 0.4 x + 40
C)f ( x )= -0.2 x + 40
D)f ( x )= 0.2 x - 40
E)f ( x )= 0.2 x + 40

Question

Quizplus · Accepted Answer

Let's use the information given to form two equations with two unknowns. Let d be the fixed amount per day and m be the amount per mile.

From the first day:
d + 300m = 100

From the second day:
d + 550m = 150

We can then solve for d in terms of m by subtracting one equation from the other:
(550m - 150) - (300m - 100) = 250m - 50 = 10d

Simplifying:
5m - d = 2

Now we have a linear equation in the form y = mx + b with m = 5 and b = -2. However, we want to solve for d as a function of m, so we rearrange the equation:

d = 5m - 2

Therefore, the function that the agency could use to determine its daily rental charges is:

f(x) = 5x - 2

Substituting x for m for clarity:

f(m) = 5m - 2

Comparing with the answer choices, we see that the correct choice is E.

Suppose That a Car Rental Agency Charges a Fixed Amount