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A truck can be rented from Company A for ​$100 a day plus ​$0.20 per mile. Company B charges ​$60 a day plus ​$0.70 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.

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Answer:

Step-by-step explanation:

First, we write the rental cost with each company:

Company A [tex]Pa = 100 + 0.2*m[/tex]

Company B [tex]Pb = 60 + 0.7*m[/tex]

Where m: miles travelled

Now, we need to find "number of miles in a day at which the rental costs for Company A and Company B are the same". This means Pa = Pb. Then:

[tex]100 + 0.2*m = 60 + 0.7*m[/tex]

Solving the equation for m by taking 0.2m and 60 on both sides:

[tex]100 + 0.2*m - 0.2*m - 60 = 60 + 0.7*m - 0.2*m - 60[/tex]

[tex] 40 = 0.5*m[/tex]

Finally, dividing 0.5 on both sides:

[tex] m = 80[/tex]

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