Begin by writing an equation for the total cost at Company C.
200 miles
Practice makes perfect
We want to find the number of miles at which the total costs are the same at Company A and Company C. Since the equation of the total cost at Company A is given in Example 3, we will begin by writing an equation for the total cost at Company C.
We will solve the system by graphing. Let's draw the graphs on the graphing calculator! We will first press the Y= button and type the functions in two of the rows. Having written the functions, we can push GRAPH to draw them.
Next we will find the point of intersection of the graphs. To do so we push 2nd and CALC and choose the fifth option, intersect. Then, we choose the first and second curve and pick a best guess for the point of intersection.
Because the graphs intersect at (200,775) the solution of the equation is x=200. Therefore, the total costs are the same after 200 miles.
Alternative Solution
Solve the Equation Algebraically
Let's consider the system of equations.
y=3.25x+125 y=3.30x+115
Since the y-variables are isolated in both equations, we can use the Substitution Method to solve this system.
3.25x+125 = 3.30x+115
Let's solve this equation algebraically.
