Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company A charges $118 and allows unlimited mileage.
Company B has an initial fee of $55 and charges an additional $0.90 for every mile driven.
For what mileages will Company A charge less than Company B?
Use for the number of miles driven, and solve your inequality for .
A = 118
B = 55+.9x
A <= B
118 <= 55 + .9x
.9x >= 63
x >= 70
Let's represent the number of miles driven as "x".
For Company A, the cost is a flat fee of $118, regardless of the number of miles driven. So, for any value of x, Company A's cost remains $118.
For Company B, the cost consists of an initial fee of $55 plus an additional charge of $0.90 for every mile driven. So, the cost for Company B can be represented as 55 + (0.90 * x).
To find the mileage at which Company A charges less than Company B, we set up the inequality:
118 < 55 + (0.90 * x)
Now, let's solve the inequality for x:
118 - 55 < 55 + (0.90 * x) - 55
63 < 0.90 * x
Divide both sides of the inequality by 0.90:
63 / 0.90 < x
70 < x
Therefore, for mileages greater than 70, Company A will charge less than Company B.
To determine the mileage at which Company A charges less than Company B, we can set up an inequality and solve for 'x' (the number of miles driven).
Let's start by setting up the equation for Company A:
Cost_A = $118
Next, let's set up the equation for Company B:
Cost_B = $55 + $0.90 * x
To find the mileage at which Company A charges less than Company B, we need to find the point where Cost_A < Cost_B.
Therefore, we have the inequality: $118 < $55 + $0.90 * x
Now, we can solve the inequality for 'x':
$118 - $55 < $0.90 * x
$63 < $0.90 * x
To isolate 'x', we need to divide both sides of the inequality by $0.90:
$63 / $0.90 < x
70 < x
So, for mileage values greater than 70 miles, Company A will charge less than Company B.
Therefore, the inequality for the number of miles driven is: x > 70