Question

Two car rental companies charge an initial rental fee plus a fee per day. The table shows the total costs of renting a car for x days from Discount Car Rentals. The total cost y (in dollars) of renting a car for x days from Pay Less Rentals is represented by the equation y=55x + 60. Which rental company charges less per day? How many days must you rent a car for the total costs to be the same?​

Answer 1

Answer:

a) Which rental company charges less per day?

Payless rental company

b) How many days must you rent a car for the total costs to be the same?​

3 days.

Step-by-step explanation:

We have car rental companies

Discount car rentals and Pay less car rentals.

x = number of days

y = Total cost.

a) Let's assume the starting day of renting a car is 2 days

We need to determine the Equation for discount rentals.

For Discount car rentals

2 days = $185

4 days = $265

6 days = $345

8 days = $425

The difference between 2 days = $265 - $185 = $80

If the difference between 2 days = $80

Difference between 1 day = $80/2

= $40

If you rent a car for 1 day,

185 - 40 =$145

Hence, the Equation for payment for Discount rentals =

y = 40x + 105

b) For Pay less car rentals

This equation was given: y = 55x + 60.

y = Total cost, x = number of days

a) 1 day

y = 55(1) + 60

y = $115

b) 2 days

y = 55(2) + 60

y = 110 + 60

y = $170

c) 3 days

y = 55(3) + 60

= 165 + 60

= $225

d)For 4 days

y = 55x + 60.

y = 55 × 4 + 60

y = 220 + 60

y = $280

e) For 5 days

y = 55x + 60.

y = 55 × 5 + 60

y = 275 + 60

y = $335

f) For 6 days

y = 55x + 60.

y = 55 × 6 + 60

y = 330 + 60

y = $380

g) For 7 days

y = 55x + 60.

y = 55 × 7 + 60

y = 385 + 60

y = $445

h) For 8 days

y = 55x + 60.

y = 55 × 8 + 60

y = 440 + 60

y = $500

a) Which rental company charges less per day?

The total coast for renting a car as determined in the above calculation

For 1 day in Discount car rentals = $145

For 1 day in Payless car rentals = $115

From the above calculation, it is Payless rental company

b) How many days must you rent a car for the total costs to be the same?

We equate both equations to each other

y = 40x + 105 = y = 55x + 60.

40x + 105 = 55x + 60

105 - 60 = 55x - 40x

45 = 15x

x = 45/15

x = 3 days.

Therefore, after 3 days, the total cost of renting a car from Discount car rentals or Payless car rentals is the same.