Answer:
The mileages for which Company A charges less than Company B is 0 miles ≤ m ≤ 85 miles
Step-by-step explanation:
The given parameters for the two companies are;
For Company A
Company A initial fee = $55
The additional fee per mile = 70 cents
For Company B
Company B initial fee = $97.50
The additional fee per mile = 20 cents
Let [tex]C_A[/tex] represent the total charge for company A and let [tex]C_B[/tex] represent the total charge for company B, we have;
[tex]C_A[/tex] = 55 + 0.70 × m
[tex]C_B[/tex] = 97.50 + 0.20 × m
Where "m" represents the number of miles driven
Therefore, the cost of Company A and Company B are the same or equal when have the following relation;
[tex]C_A[/tex] = [tex]C_B[/tex]
∴ 55 + 0.70 × m = 97.50 + 0.20 × m
0.70 × m - 0.20 × m = 97.50 - 55
0.5 × m = 42.5
m = 85
The number of miles driven for which the two companies will charge the same amount, m = 85 miles
Therefore, given that the initial fee for Company A is less than the initial fee for Company B. we have;
Therefore for 0 miles ≤ m < 85 miles, Company A charges less than Company B.
