a The total cost is a sum of a flat rate and the variable cost.
B
b The total cost is a sum of a flat rate and the variable cost.
C
c Use the functions found before and compare the costs of the trip.
A
a
C_P(m)=18+0.32m
B
b
C_Y(m)=12+0.36m
C
c
Proxy
Practice makes perfect
a The total cost of renting a car from Proxy, C_P, is the sum of a surcharge and a variable cost. We can rewrite this as an equation.
C_P=surcharge+variable cost
Since we know that the surcharge is equal to $ 18, we can substitute 18 into our equation.
C_P= 18+variable cost
The variable cost is equal to a charge per mile, $0.32, that is multiplied by the number of miles driven, m.
variable cost=0.32* m
Using the Substitution Property, we can substitute 0.32m for variable cost in our equation. We then get the equation for the total cost of renting from Proxy.
C_P=18+ 0.32m
Since we want it to be a function, we will replace C_P with C_P(m), which emphasizes that the total cost of renting a car depends on m.
C_P(m)=18+0.32m
b Similary, the total cost of renting a car from YourPal, C_Y, is also the sum of a surcharge and a variable cost. We can rewrite it as an equation.
C_Y=surcharge+variable cost
Since we know that the surcharge is equal to $ 12, we can substitute 12 into our equation.
C_Y= 12+variable cost
The variable cost is equal to the charge per mile, $0.36, multiplied by the number of miles driven, m.
variable cost=0.36* m
Again, we can use the Substitution Property and substitute 0.36m for variable cost in our equation. We then get the equation for the total cost of renting a car from Proxy.
C_Y=12+ 0.36m
Since we want it to be a function, we will replace C_Y with C_Y(m), which emphasizes that the total cost of renting depends on the numbers of mile driven, m.
C_Y(m)=12+0.36m
c Now that we have functions for the total cost of renting a car from each company, we will calculate the cost of a 820 mile trip. Insert 820 into each function, then calculate and compare to tell which deal is better. Let's start with Proxy rental company.
The total cost of renting a car from YourPal for an 820-mile trip is equal to $307.20. Since 307.2> 280.4, it is better to rent a car from Proxy for a 820 mile trip.
