I tried this and needed to graph. But, I want to find out what I did incorrect.
Suppose that a car rental agency gave you the following choices.
Option A: $30 per day plus 40 cents per mile.
Option B: flat $50 per day
(a) Write equations for cost per day c for options A and B. (Use m for distance in miles)
(b) Graph the equations for options A and B
c= $30.00 plus 40 cents = 30. + .04= 34.00 (option A)
c= $50.00 (option B)
(c) Estimate the mileage for which both rates are the same. m = 20 miles?
Would this be graphed as: 34 and 50?
You want 30+.4m=50
.4m = 20
m = 50
SO, if you drive 50 miles, A and B cost the same.
To determine what you did incorrectly, let's go through the problem step by step.
(a) Writing equations for the cost per day for options A and B:
Option A: cost per day (c) = $30.00 + 0.40 * distance in miles (m)
Option B: cost per day (c) = $50.00
You correctly wrote the equation for option A as c = $30.00 + 0.40m, which is the correct representation for Option A.
However, you stated that the cost per day for Option B is $34.00, which is incorrect. The correct equation for Option B is simply c = $50.00 since it is a flat fee.
(b) Graphing the equations for options A and B:
To graph the equations, we'll need to assign the x-axis to represent the distance in miles (m) and the y-axis to represent the cost per day (c).
For Option A: c = 30.00 + 0.40m, we can start by plotting a few points. Let's say for m = 0, c = 30.00, and for m = 10, c = 34.00 (as you calculated incorrectly). You can choose more values if you'd like. Plot these points and draw a line through them to represent Option A.
For Option B: c = 50.00, we have a flat line at y = 50.00. Draw a horizontal line representing Option B.
(c) Estimating the mileage for which both rates are the same:
To find the mileage when the rates are the same, we need to find the intersection point of the two graphs. In this case, we want to find the value of m that makes c for both options equal.
On the graph, find where the line representing Option A (y = 30.00 + 0.40m) intersects with the line representing Option B (y = 50.00). The x-coordinate of this point represents the mileage (m) at which both rates are the same.
The estimated mileage for which both rates are the same appears to be around m = 20 miles, based on your suggestion. However, it's better to find the exact value by solving the equation: 30.00 + 0.40m = 50.00.
In summary, the correct graph would have Option A represented by a line starting at (0, 30.00) and ascending with a slope of 0.40, while Option B is a horizontal line at y = 50.00. The intersection point between the two lines represents the mileage at which both rates are equal.