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

Answer:

a) Which rental company charges a lower daily rate?

Payless rental company.

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

3 days.

Step-by-step breakdown:

We are comparing two rental services:

Discount Car Rentals and Payless Car Rentals.

x = rental duration in days

y = total cost.

a) Assuming the rental period starts at 2 days:

We need to formulate the equation for Discount Rentals.

For Discount Car Rentals:

2 days = $185

4 days = $265

6 days = $345

8 days = $425

The cost differential for 2 days = $265 - $185 = $80

Therefore, for 1 day the cost difference is = $80/2

= $40

For a one-day rental,

185 - 40 = $145

Thus, the equation for the payment of Discount Rentals is:

y = 40x + 105

b) For Payless Car Rentals:

The provided equation is: y = 55x + 60.

y = total cost, x = rental days

a) For 1 day:

y = 55(1) + 60

y = $115

b) For 2 days:

y = 55(2) + 60

y = 110 + 60

y = $170

c) For 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 a lower daily rate?

The total expense of renting a vehicle as calculated above:

For 1 day from Discount Car Rentals = $145

For 1 day from Payless Car Rentals = $115

Based on these calculations, Payless rental company offers the lower rate.

b) For how many days is the rental required to have costs equal?

We set both equations equal 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.

Hence, after 3 days, the total cost of renting a vehicle from either Discount or Payless Car Rentals will be equal.