Best Car rental agency charges a flat rate of $40 and 10¢ per mile to rent a standard car. A+ Rentals charges a flat rate of $35 and 20¢ per mile for the same car.
a. Write an equation to represent the total cost (y) and number of miles (x) of renting from each company.
b. If you plan to rent a car and travel 500 miles, which plan would you choose and why? Show your work.
c. How many miles do you need to drive for both plans to cost the same?
a. Best = y = 40 + .10x
A+ = y = 35 + .20x
b. Calculate y when x = 500.
c. 40 + .10x = 35 + .20x
Solve for x.
25.DOLLARS A DAY .10 CENT A MILE AND 40.00 DOLLARS A DAY .10 CENT A MILE
a. Let's write the equations to represent the total cost (y) and number of miles (x) of renting from each company:
For Best Car rental agency:
Total cost (y) = flat rate + (mileage rate * number of miles)
y = $40 + $0.10x
For A+ Rentals:
Total cost (y) = flat rate + (mileage rate * number of miles)
y = $35 + $0.20x
b. To find out which plan would be cheaper for renting a car and traveling 500 miles, we can substitute x = 500 into the equations and compare the total costs.
For Best Car rental agency:
y = $40 + $0.10 * 500
y = $40 + $50
y = $90
For A+ Rentals:
y = $35 + $0.20 * 500
y = $35 + $100
y = $135
Comparing the total costs, we can see that Best Car rental agency would cost $90 and A+ Rentals would cost $135 for renting a car and traveling 500 miles.
Based on this calculation, it would be more affordable to choose the plan from Best Car rental agency, as it would cost $45 less than A+ Rentals.
c. To find out how many miles you would need to drive for both plans to cost the same, we can set the two equations equal to each other and solve for x.
$40 + $0.10x = $35 + $0.20x
Simplifying the equation, we get:
$40 - $35 = $0.20x - $0.10x
$5 = $0.10x
Dividing both sides of the equation by $0.10, we find that:
x = 50
Therefore, you would need to drive 50 miles for both plans to cost the same.