SOLUTION: 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 additiona

Question 1123847: 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)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x = the number of hours of rental.

company A charges 70 + 4x

company B charges 60 + 5x

for a 6 hour rental:

A charges 70 + 4*6 = 70 + 24 = 94
B charges 60 + 5*6 = 60 + 30 = 90

for a 7 hour rental:

A charges 70 + 4*7 = 70 + 28 = 98
B charges 60 + 5*7 = 60 + 35 = 95

company B charges less for both the 6 hour rental and the 7 hour rental.

for the 7 hour rental, company B charges 3 dollars less than company A.

your solution appears to be:

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)

equations are c = 70 + 4x for company A and c = 60 + 5x for company B.
c is the total charges.
x is the number of hours that the trucks are being rented for.

Part B: Which company would charge less for renting a truck for 6 hours? Justify your answer. (3 points)

company B would charge less.
the fixed charges for company B are 10 dollars less than the fixed charges for company A (60 versus 70).
the variable charges for company B are 30 and the variable charges for company A are 24.
company B charges 6 dollars more for the variable part of the charges (the per hour charges).
company B charges 10 dollars less for the fixed portion of the charges, but 6 dollars more for the variable portion of the charges.
this means company B charges a net 4 dollars less total.

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)

company B charges 10 dollars less for the fixed portion of the charges 70 for company A and 60 for company B), but charges 7 dollars more for the variable portion of the charges (28 for company A and 35 for company B).
company B charges a net 3 dollars less than company A (10 - 7).

for your additional information, see below:

the break even point is when company A charges the same as company B.

in that case, 70 + 4x = 60 + 5x.
subtract 60 from both sides of that equation and subtract 4x from both sides of that equation to get 70 - 60 = 5x - 4x
combine like terms to get 10 = x
the break even point is at 10 hours.

for a 10 hour rental:

company A charges 70 + 4*10 = 110
company B charges 60 + 5*10 = 110

for a rental that lasts less than 10 hours, company B is cheaper.
for a rental that lasts more than 10 hours, company A is cheaper.

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