You were given two options of cars to rent to drive to California with renting prices listed below.
The Honda Civic would cost $15 plus $0.50 per mile driven.
The Ford Focus would cost $25 plus $0.25 per mile driven.
Create an inequality to represent any number of miles for which the Honda Civic would be the better renting option. Explain what your inequality means.
I know that anything greater than 40 miles is a better deal for the Honda Civic, but how do i structure the inequality?
Correct
To structure the inequality, let's start by assigning a variable to represent the number of miles driven. Let's use "m" for this.
Now, let's determine the cost of renting both cars based on the given information:
For the Honda Civic, the total cost "C1" can be calculated using the formula: $15 + ($0.50 * m).
For the Ford Focus, the total cost "C2" can be calculated using the formula: $25 + ($0.25 * m).
To represent the scenario where the Honda Civic is the better renting option, we can set up the inequality:
C1 < C2
Substituting the cost formulas in the inequality, we have:
$15 + ($0.50 * m) < $25 + ($0.25 * m)
Now, let's simplify the inequality:
$15 + $0.50m < $25 + $0.25m
Combining like terms, we get:
$0.50m - $0.25m < $25 - $15
$0.25m < $10
To isolate the variable "m," we divide both sides of the inequality by $0.25:
m < $10 / $0.25
m < 40
The inequality m < 40 represents any number of miles for which the Honda Civic would be the better renting option. It means that if the number of miles driven is less than 40, the cost of renting the Honda Civic would be less than the cost of renting the Ford Focus.
To find the threshold at which the Honda Civic becomes the better option, we need to compare the costs of both cars based on the number of miles driven.
Let's assume x represents the number of miles driven.
Cost of renting the Honda Civic = $15 + $0.50x
Cost of renting the Ford Focus = $25 + $0.25x
The inequality to represent any number of miles for which the Honda Civic would be the better option can be written as:
$15 + $0.50x < $25 + $0.25x
Now, let's simplify the inequality:
$0.50x - $0.25x < $25 - $15
$0.25x < $10
Dividing both sides of the inequality by 0.25, we get:
x < $10 / $0.25
x < 40
The inequality x < 40 means that for any number of miles less than 40, the Honda Civic would be the better renting option. Therefore, to be more cost-effective than the Ford Focus, the number of miles driven with the Honda Civic must be less than 40.
Honda: y = 15 + .50x
Ford: y = 25 + .25x
15 + .50x = 25 + .25x
Subtract 15 from both sides:
.50x = 10 + .25x
Subtract .25x from both sides:
.25x = 10
Divide by .25, gives you x = 40