Austin is comparing the prices of two truck rental companies. Company A charges $4 per hour and an additional $70 as service charges. Company B charges $5 per hour and an additional $60 as service charges. Part A: Write an equation to represent each company's total charges for renting a truck for a certain number of hours. For both equations (one for Company A and one for Company B), define the variable used. (4 points) Part B: Which company would charge less for renting a truck for 6 hours? Justify your answer. (3 points) Part C: How much money is saved by using the services of Company B instead of Company A to rent a truck for 7 hours? (3 points)

For Part A:
(H = # of hours, t = total cost)

Company A: 4h + 70 = t
Company B: 5h + 60 = t

Part B:
It actually depends on how long you plan to rent a truck. There is a period of time where the cost for renting the truck is the same. It's at the 10 hour mark. Plug 10 hours into the equation like so:

4*10 + 70 = $110
5*10 + 60 = $110

As you can see, the cost is exactly the same at 10 hours. Now, let's try plugging in a number lower and higher than 10 hours and see what we get.

9 hours:

4*9 + 70 = $106
5*9 + 60 = $105 (as you can see, Company B barely costs less at this point)

11 hours:

4*11 + 70 = $114 (now Company A is barely cheaper than the Company B)
5*11 + 60 = $115

So, if you were to rent a truck for 10 hours or less, Company B would be cheaper. If you were to rent a truck for more than 10 hours, Company A would become cheaper.

Part C:
Simply plug 7 hours into both of our equations like shown below.

4*7 + 70 = $98
5*7 + 60 = $95

Now subtract $95 from $98 to get $3. You would save three dollars renting a truck with Company B

I hope this helps you! If I missed something, please notify me right away :)