Question

Arthur is comparing the prices of two car rental companies. Company A charges $22 per day and an additional $5 as service charges. Company B charges $20 per day and an additional $16 as service charges.

Part A: Write an equation to represent each company's total charges for renting a car for a certain number of days. For both equations (one for Company A and one for Company B), define the variable used.

Part B: Which company would charge less for renting a car for 9 days? Justify your answer.

Part C: How much money is saved by using the services of Company B instead of Company A to rent a car for 15 days?

Answer 1

Company A
f(d) = 22×d + 5

Company B
g(d) = 20×d + 16

The variable used is d (stands for days).

f(9) = 22×9 +5 =203
g(9) = 20×9 + 16 = 196

Company B is cheaper.
22d + 5 = 20d + 16
2d = 11
d = 5.5
Even though Company B has a higher starting fee, it is cheaper after 5.5 days because it has a lower daily rate.

f(d) - g(d)
= (22d + 5) - (20d + 16)
= (22d - 20d) + (5 - 16)
= 2d - 11
Plug in 15
= 2×15 - 11
= 30 - 11
= 19

Answer 2

Part A:

Company A formula is 22d+5
Company B formula is 20d+16
the variable used is d, which represents the number of days

Part B:
Company A: 22(9)+5 = $203
Company B: 20(9)+16= $196
So company A is cheaper

Part C:
Company A: 22(15)+5= $335
Company B: 20(15)+ 16= $316
335-316= 19
$19 is saved