Solve and show all your work/steps to receive full credit. (5 points)%0D%0AA truck can be rented from Company A for $80 a day plus $0.30 per mile. Company B charges $50 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same
Let's assume the number of miles in a day as "x".
The rental cost for Company A is $80 for a day plus $0.30 per mile:
Cost for Company A = $80 + $0.30x
The rental cost for Company B is $50 for a day plus $0.60 per mile:
Cost for Company B = $50 + $0.60x
Now, we need to find the number of miles in a day at which the rental costs for Company A and Company B are the same, so we set up the equation:
$80 + $0.30x = $50 + $0.60x
First, let's simplify the equation by moving all the terms with "x" to the left side and the constant terms to the right side:
$0.30x - $0.60x = $50 - $80
Now, let's combine like terms:
-$0.30x = -$30
To isolate "x", let's divide both sides of the equation by -0.30:
x = $30 / (-0.30)
x = -100 miles
Therefore, the rental costs for Company A and Company B are the same when the number of miles in a day is -100 miles. However, this does not make sense in real-world scenarios, so there is no practical solution to this equation.