I need help solving these two problems

May 13th, 2015
KateS
Category:
Algebra
Price: $10 USD

Question description

Question 1

Part1

You want to celebrate all of your recent successes.  You decide to reward yourself and a special someone with a vacation to a destination of your choosing.  For your trip you will need to stay in a hotel/resort and rent a car.

You decide to rent a car for the duration of your trip.  You have two options.  Write an equation for each company that depicts the total cost of the rental, y, based on the number of days, x.

Cheepers Rent-A-Car:

$39/day with a one-time charge of $20 for insurance/fees

Busters:

$49/day but all additional fees are included in the price of the rental

Be sure to label each equation with the company it corresponds to.

Part 2

Graph the system of equations that you wrote for car rental options to determine the break-even point for the cost of the car rentals.  One easy way to do this is using desmos.com, the online graphing calculator and take a screen shot of your graph.  If you are unsure how to capture a screen shot visit http://www.take-a-screenshot.org/.  You may also choose to graph this by hand and take a picture of your graph but be sure that your graph is easy to read.  Insert either option AS A PICTURE using the  button.

Part 3

Write your solution to the system as an ordered pair, then interpret the values in the context of the problem.

Part 4

Explain how you would use your graph to determine the cheaper option after one day, two days, three days etc.  What would you look for on the graph?

Part 5

Explain how you would use your break even point to determine the cheaper option after one day, two days, three days etc. 

Question 2

Part 1

You also have two options for lodging.  Write an equation FOR EACH OPTION that depicts the total cost of your stay, y, based on the number of days, x.

Bilton Hotel:

$100/night but you must pay an additional one-time fee of $40 for parking and other fees

Triple Tree:

$110/night with no additional parking or resort fees.

Be sure to label each equation with the hotel it corresponds to.

Part 2

You will need to use either substitution or elimination to solve this system.  Which method will you choose?  What factors helped you make that decision?

Part 3

Show your work for solving the system of equations you wrote for your hotel options using the equation editor.  Be sure to use the method you decided on in the previous question.

Part 4

 Write your solution to the system as an ordered pair, then interpret the values in the context of the problem.


Tutor Answer

(Top Tutor) Daniel C.
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School: UCLA
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