Hondas rent for $25 per day and $.24 (24 cents) per mile.
Toyotas rent for $31 per day and $.19 (19 cents) per mile.
Write a cost equation for each rental car The distance from Monterey, Ca to San Francisco, Ca is about 110 miles. Which car would be the better choice to rent for a one-way drive to San Francisco from Monterey?
Which car would be the better choice to rent for a round-trip drive from Monterey to San Francisco and back?
What is the break-even point for both rental cars, include the mileage and cost.
My answer for the first part: Let x = number of miles driven. Let y = cost to rent cars
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l70970
To calculate the cost of renting each car, we can use the given information:
For the Honda:
Cost per day = $25
Cost per mile = $0.24
The cost equation for the Honda would be:
Cost = $25 (day) + $0.24 (mileage)
For the Toyota:
Cost per day = $31
Cost per mile = $0.19
The cost equation for the Toyota would be:
Cost = $31 (day) + $0.19 (mileage)
Now let's use these equations to determine which car would be the better choice for different scenarios.
1. One-way drive from Monterey to San Francisco:
Given that the distance from Monterey to San Francisco is 110 miles, we can substitute x = 110 into the cost equations for both cars and compare the results to find the cheaper option.
For the Honda:
Cost = $25 (day) + $0.24 (110 miles)
Cost = $25 + $26.40
Cost = $51.40
For the Toyota:
Cost = $31 (day) + $0.19 (110 miles)
Cost = $31 + $20.90
Cost = $51.90
In this case, the Honda would be the better choice as it is slightly cheaper.
2. Round-trip drive from Monterey to San Francisco and back:
Since this is a round-trip, the distance traveled would be double the one-way distance, which is 220 miles. We can substitute x = 220 into the cost equations and compare the results.
For the Honda:
Cost = $25 (day) + $0.24 (220 miles)
Cost = $25 + $52.80
Cost = $77.80
For the Toyota:
Cost = $31 (day) + $0.19 (220 miles)
Cost = $31 + $41.80
Cost = $72.80
In this case, the Toyota would be the better choice as it is cheaper.
3. Break-even point:
To find the break-even point for both rental cars, we can set the cost equations equal to each other and solve for x (mileage).
For the Honda and Toyota:
$25 + $0.24x = $31 + $0.19x
Simplifying the equation:
$0.05x = $6
x = $6 / $0.05
x = 120 miles
Therefore, the break-even point for both rental cars is 120 miles. If you drive more than 120 miles, the Toyota would be cheaper, and if you drive less than 120 miles, the Honda would be cheaper.