Answer to Question #5496 in Algebra for Jane

Question

#51. A rental company charges $40.00 a day plus $0.35 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y=0.35x+40. A second company charges $36.00 a day plus $0.45 per mile, so the daily cost, y, if x miles are driven is described by y=0.45x+36. The graphs of the two equations are shown in the same rectangular coordinate system.

a. What is the x-coordinate of the intersection point of the graphs? Decribe what the x-coordinate means in practical terms.

Answer 1

Let's solve the following system of equations:

y=0.35x+40
y=0.45x+36

0.35x+40 = 0.45x+36
4 = 0.1x
x = 40
y = 0.35*40+40 = 54

So, (x,y) = (40,54) - point of intersection.

That point is the point of payment equality: you can take a truck and drive it 40 miles, the price will be the same for both first and second companies - $54.