Answer:
- Discount car rentals charges less daily
- After 3 days
Step-by-step explanation:
Required
Which charges less per day
When is the total cost the same
First, calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
From the table, we have:
[tex](x_1,y_1) = (2,185)[/tex]
[tex](x_2,y_2) = (6,345)[/tex]
So, we have:
[tex]m = \frac{345 - 185}{6 - 2}[/tex]
[tex]m = \frac{160}{4}[/tex]
[tex]m = 40[/tex]
The equation is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 40(x - 2) + 185[/tex]
[tex]y = 40x - 80 + 185[/tex]
[tex]y = 40x + 105[/tex]
So, the equation of the table (i.e. Discount Car rental) is: [tex]y = 40x + 105[/tex]
While the equation of Pay Less is: [tex]y = 55x + 60[/tex]
The company that charges less per day has the smaller slope and that is: Discount car rental because the slope (40) is less than the slope (55)
For the total cost to be the same, we simply equate both expressions:
i.e.
[tex]y = y[/tex]
[tex]55x + 60 = 40x + 105[/tex]
[tex]55x - 40x = - 60 + 105[/tex]
[tex]15x =45[/tex]
[tex]x = 3[/tex]
