Math Task 5

Part A

Olivia will soon be going to college. She is looking to secure a hard copy of the required book for her math class. Rent A Book offers weekly rental rates at 5 dollars a week as well as a purchase option for a flat rate of 75 dollars. There is also a processing fee of 10 dollars per order. If Olivia's class is 2 months long, which option best meets her needs and would be the cheapest option?
*One month = 4 weeks

Part B

Option A = Rent textbook at $5 week plus $10 processing fee
Option B = Purchase textbook at flat rate of $75 plus $10 processing fee

Option A equation: y = 5x + 10
Option B equation: y = 75 + 10

Y = Total cost
X = Number of weeks

Since we need to solve for total cost, based on the number of weeks and how the company charges in this situation, we will let Y = the total cost to Alexis Livia and X represent the number of weeks needed. This will allow us to solve for the cost at any given number of weeks.

In order to determine when the two options would be equivalent, we will use the substitution method.

y = 5x +10 and y = 75 + 10 becomes 5x + 10 = 75 + 10

5x + 10 = 75 + 10
5x + 10 (-10) = 75 + 10 (-10) Isolate x by subtracting 10 from both sides
5x/5 = 75/5 Divide each side by 5 to solve for x x = 15

Therefore it would be 15 weeks when it would cost the same amount of money to either rent the text book per week or purchase the text book at a flat rate.

Since we have solved for x above (number of weeks), in order to determine the ordered pair, we solve the equation which contains x, substituting for x.

y = 5x +10 15 is substituted for x in the equation y = 5(15) + 10 Multiply y = 75 + 10 Add y = 85
Ordered Pair is (15, 85)

Part C

Please see graph in separate file

Part D

Olivia only needs the text book for 2 months or 8 weeks. Using the mathematical equation above to figure out the price for 8 weeks, she would spend a total of $50.00 on a rental vs