"The university of Oklahoma maintains a fleet of vehicles to rent to university departments. To transport equipment, the School of Drama needs to rent either a cargo can or a pickup truck for one day. The cargo van costs $28 for a day, plus $0.22 per mile. The pickup truck costs $29 for a day plus $0.17 per mile. For what mileage is the cost the same?"
I'm supposed to work this out with systems of equations, but I can't seem to figure out anything that works. Please help me word this problem!
28 + .22m = 29 + .17m
Solve for m.
To solve this problem using systems of equations, we need to first define the variables and set up the equations based on the given information.
Let's assume the mileage for which the cost is the same is represented by 'x' miles.
For the cargo van option, the rental cost per day is $28 and the cost per mile is $0.22, so the total cost can be represented by the equation:
Cost of cargo van = $28 + ($0.22 * x)
For the pickup truck option, the rental cost per day is $29 and the cost per mile is $0.17, so the total cost can be represented by the equation:
Cost of pickup truck = $29 + ($0.17 * x)
Now, we can set up the equation to find the mileage where the cost is the same:
$28 + ($0.22 * x) = $29 + ($0.17 * x)
To solve this equation, we can use algebraic methods like combining like terms and isolating the variable 'x'.
Let's simplify the equation:
$0.22 * x - $0.17 * x = $29 - $28
Combining like terms:
$0.05 * x = $1
Now, divide both sides of the equation by $0.05 to isolate 'x':
x = $1 / $0.05
Simplifying the right side:
x = 20
Therefore, the cost will be the same for both the cargo van and the pickup truck when the mileage is 20 miles.
You can double-check this answer by substituting the value of 'x' (20 miles) into the original equations and verifying that the costs are equal in both cases.