Question

Amanda is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.

Answer 1

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 $C_A$ represent the total charge for company A and let $C_B$ represent the total charge for company B, we have;

$C_A$ = 55 + 0.70 × m

$C_B$ = 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;

$C_A$ = $C_B$

∴ 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.