Question

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.

Answer 1

Explanation:

First, we write the rental cost with each company:

Company A
`Pa = 100 + 0.2*m`

Company B
`Pb = 60 + 0.7*m`

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:

`100 + 0.2*m = 60 + 0.7*m`

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

`100 + 0.2*m - 0.2*m - 60 = 60 + 0.7*m - 0.2*m - 60`

`40 = 0.5*m`

Finally, dividing 0.5 on both sides:

`m = 80`