A truck can be rented from Company A for $70 a day plus $0.40 per mile. Company B charges $30 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's?
y =70 + .40x
y = 30 + .80x
70 + .40 x < 30 + .80x
-.40x < -40
x > 100
When you multiply or divided across an inequality by a negative, you change the direction of the inequality.
A truck can be rented from company a for $70 a day plus .50 per mile company b charges $40 a day plus 0.60
To determine when the rental cost for Company A becomes a better deal than Company B's, we need to find the number of miles driven in a day for which the two costs are equal. Let's call this number of miles x.
For Company A:
The cost of renting from Company A per day is $70, and the cost per mile is $0.40. Therefore, the total cost for renting from Company A for a day with x miles driven can be expressed as:
Total cost for Company A = $70 + $0.40x
For Company B:
The cost of renting from Company B per day is $30, and the cost per mile is $0.80. Therefore, the total cost for renting from Company B for a day with x miles driven can be expressed as:
Total cost for Company B = $30 + $0.80x
To find the breakeven point, we need to equate the total costs for both companies:
$70 + $0.40x = $30 + $0.80x
Now, let's solve this equation to find the value of x:
$0.40x - $0.80x = $30 - $70
- $0.40x = - $40
x = (-$40) / (- $0.40)
x = 100
Therefore, for x = 100 miles driven in a day, the rental cost for Company A becomes a better deal than Company B's.
To determine the number of miles that must be driven in a day to make the rental cost for Company A a better deal than Company B's, we need to find the point at which the cost for Company A becomes less than the cost for Company B.
Let's set up an equation to represent the cost for both companies:
Cost for Company A = $70 + $0.40 per mile
Cost for Company B = $30 + $0.80 per mile
Now, we need to find the number of miles, denoted by "x," at which the cost for Company A becomes less than the cost for Company B.
For this, we'll set up an inequality:
$70 + $0.40x < $30 + $0.80x
Now, let's solve this inequality step-by-step to find the value of x.
Starting with the inequality:
$70 + $0.40x < $30 + $0.80x
Subtract $0.40x from both sides:
$70 < $30 + $0.40x
Subtract $30 from both sides:
$40 < $0.40x
Divide both sides by $0.40:
$100 < x
Therefore, to make the rental from Company A a better deal than Company B's, the number of miles driven in a day must be greater than $100.