A truck can be rented from Company A for $90 a day plus $0.70 per mile. Company B charges $60 a day plus $0.80 per mile to rent the same truck. How many miles must be driven in a day to make the rental cost for Company A a better deal than Company B?
90 + .7 m < 60 + .8 m
30 < .1 m
300 < m
90+.7m<60+.8m
To determine when the rental cost for Company A becomes a better deal than Company B, we need to compare the total cost for each company.
Let's represent the number of miles driven in a day as "m".
For Company A:
Rental cost per day = $90
Cost per mile = $0.70
Total cost for Company A = Rental cost per day + (Cost per mile * Number of miles driven)
Total cost for Company A = $90 + ($0.70 * m)
Total cost for Company A = $90 + 0.70m
For Company B:
Rental cost per day = $60
Cost per mile = $0.80
Total cost for Company B = Rental cost per day + (Cost per mile * Number of miles driven)
Total cost for Company B = $60 + ($0.80 * m)
Total cost for Company B = $60 + 0.80m
We need to find when the total cost for Company A is less than the total cost for Company B.
Mathematically, we can set up the following inequality:
$90 + 0.70m < $60 + 0.80m
To determine the number of miles required, we can solve the inequality:
0.10m < $60 - $90
0.10m < -$30
m < -$30 / 0.10
m < -300
Since the number of miles driven cannot be negative, we ignore the negative solution. Thus, the truck must be driven more than 300 miles in a day for Company A to be a better deal than Company B.
To determine the number of miles that must be driven in a day for the rental cost of Company A to be a better deal than Company B, we can set up an equation.
Let's assume the number of miles driven in a day is represented by 'm'.
For Company A:
Cost = $90 (base daily rental fee) + $0.70 (cost per mile) * m
For Company B:
Cost = $60 (base daily rental fee) + $0.80 (cost per mile) * m
We need to find the value of 'm' for which the cost of Company A is less than the cost of Company B.
Using the equation:
$90 + $0.70 * m < $60 + $0.80 * m
Rearranging the equation:
$90 - $60 < $0.80 * m - $0.70 * m
$30 < $0.10 * m
Dividing both sides by $0.10:
300 < m
So, in order for the rental cost for Company A to be a better deal than Company B, you must drive more than 300 miles in a day.