## You need to rent a video camera for your school project. Murphy’s Camera charges a $30 rental fee plus $35 per day. Allied Rental charges a

You need to rent a video camera for your school project. Murphy’s Camera charges a $30 rental fee plus $35 per day. Allied Rental charges a $45 rental fee plus $30 per day. Which company should you choose?

Independent variable (x):

Dependent variable (y):

System of equations:

Graph:

A. When does it make sense to rent a camera from Murphy’s? How do you know?

B. When does it make sense to rent a camera from Allied Rental? How do you know?

C. Is there ever a time where it wouldn’t matter which store to choose? Explain what this means in the context of a “system of equations.”

D. If you were renting a camera for 3 days, how much money would you pay for each store? Show all work.

## Answers ( )

A. If a camera is rented for 1 or 2 days, it would be logical to rent it from Murphy’s.B. If a camera is needed for more than 3 days, it would make sense to rent it from Allied rental.C. Yes, if a camera is rented for 3 days both rentals charge the same money.C. If you were need a camera for 3 days, you would have to pay $135 for both stores.Step-by-step explanation:Step 1;Murphy’s camera costs $30 to rent and an additional $35 for each day of rental. So theequationsarey = $30 + (x × $35), where y is total cost and x is the number of days rented.So for x = 1, y = $30 + (1 × $35) = $30 + $35 = $65So for x = 2, y = $30 + (2 × $35) = $30 + $70 = $100So for x = 3, y = $30 + (3 × $35) = $30 + $105 = $135So for x = 4, y = $30 + (4 × $35) = $30 + $140 = $170

So for x = 5, y = $30 + (5 × $35) = $30 + $175 = $ 205.

Step 2; Allied rental costs $45 to rent and a $30 for each day of rental. So the

equationsare as followsy = $45 + (x × $30), where y is total cost and x is the days rentedSo for x = 1, $45 + (1 × $30) = $45 + $30 = $75

So for x = 2, $45 + (2 × $30) = $45 + $60 = $105

So for x = 3, $45 + (3 × $30) = $45 + $90 = $135So for x = 4, $45 + (4 × $30) = $45 + $120 = $165So for x = 5, $45 + (5 × $30) = $45 + $150 = $195Step 3; Comparing both prices over 5 days. Murphy’s is cheaper for until 2 days. On day 3 both the rentals cost the same but after day 4, allied rentals is the better option.