The number of miles for same rental costs are 300 miles.
Let the number of miles be x.
Firstly calculating the cost of Company a -
Total cost = One day cost + Number of miles × Cost per mile
Total cost = 110 + 0.70x
Calculating the cost of Company b -
Total cost = One day cost + Number of miles × Cost per mile
Total cost = 80 + 0.80x
Now, for the same rental cost, we will equate the two expressions. This will calculate the value of x.
110 + 0.70x = 80 + 0.80x
Rearranging the expression -
110 - 80 = 0.80x - 0.70x
Performing subtraction
30 = 0.10x
Shifting the values on other side of equation
x = 30/0.10
Performing division
x = 300
Hence, the rental cost for both companies will be same for 300 miles.
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