EZ car rental charges $40 dollars a day plus $0.25 per mile. Ace Rent-A-Car charges $25 dollars a day plus $0.45 per mile. What number of miles results in the same costs as one day?

Find an expression for each Rental car company's charge in one day where x = the number of miles driven.
EZ car rental: 0.25x + 40
Ace Rent-a-car: 0.4x + 25

You want to find when the two expressions are equal, so set the two expressions equal:
0.25x + 40 = 0.40x + 25
Solve for x!

0.25x + 15 = 0.40x
15 = 0.15x
x = 15/0.15
x = 100

You can check by plugging the number back in:
0.25 (100) + 40 = 65
0.4 (100) + 25 = 65

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ApusApus ApusApus · Answer 2 · 2019-10-04T17:19:38+02:00

Answer:

75 miles.

Step-by-step explanation:

Let x represent number of miles.

We have been given that EZ car rental charges $40 dollars a day plus $0.25 per mile. The total cost of renting a car for x miles would be [tex]0.25x+40[/tex].

We are also told that Ace Rent-A-Car charges $25 dollars a day plus $0.45 per mile. The total cost of renting a car for x miles would be [tex]0.45x+25[/tex].

To find the number of miles, when both companies will cost same, we will equate both expressions and solve for x.

[tex]0.45x+25=0.25x+40[/tex]

[tex]0.45x-0.25x+25=0.25x-0.25x+40[/tex]

[tex]0.20x+25=40[/tex]

[tex]0.20x+25-25=40-25[/tex]

[tex]0.20x=15[/tex]

[tex]\frac{0.20x}{0.20}=\frac{15}{0.20}[/tex]

[tex]x=75[/tex]

Therefore, 75 miles results in the same costs as one day.