91Ó°ÊÓ

Finals are over and you are moving back home for the summer. You need to rent a truck to move your possessions from the college residence hall. You contact two local rental companies and get the following information for the 1 -day cost of renting a truck. Company \(1: \$ 39.95\) per day plus \(\$ 0.19\) per mile Company \(2: \$ 19.95\) per day plus \(\$ 0.49\) per mile Let \(x\) represent the number of miles driven in one day. a. Write an equation that represents the total cost in dollars of renting a truck for 1 day from Company 1. b. Write an equation that represents the total cost in dollars of renting a truck for 1 day from Company 2 c. Using the equations in parts a and b, write a single equation to determine the mileage for which the cost would be the same from both companies. d. Solve the equation in part \(c\) and interpret the result. e. You actually live 90 miles from the campus. Which rental company would be the better deal?

Step by step solution

01

Find the total cost equation for Company 1

We are given that Company 1 charges \(39.95 per day plus \)0.19 per mile. Let C1(x) be the total cost from Company 1 and x be the miles driven. Write the equation as: C1(x) = 39.95 + 0.19x. #b#

02

Find the total cost equation for Company 2

We are given that Company 2 charges \(19.95 per day plus \)0.49 per mile. Let C2(x) be the total cost from Company 2 and x be the miles driven. Write the equation as: C2(x) = 19.95 + 0.49x. #c#

03

Find the equation representing equal costs for both companies

To find the mileage when the cost would be the same for both companies, set C1(x) equal to C2(x): 39.95 + 0.19x = 19.95 + 0.49x. #d#

04

Solve the equation for equal costs

To solve the equation, first subtract 19.95 from both sides: 20 = 0.3x. Divide by 0.3: x = 66.67 miles. This means that the cost would be the same for both companies if you drive 66.67 miles. #e#

05

Determine which company is the better deal for 90 miles

Since you need to drive 90 miles, find the cost for each company: C1(90) = 39.95 + (0.19)(90) = 56.05\(, and C2(90) = 19.95 + (0.49)(90) = 63.55\). Since the cost of renting from Company 1 is cheaper for 90 miles, Company 1 would be the better deal.

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