David is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices.
Company $A$ charges $\$ 79$ and allows unlimited mileage.
Company $B$ has an initial fee of $\$ 65$ and charges an additional $\$ 0.70$ for every mile driven.
For what mileages will Company A charge less than Company B?
Use $m$ for the number of miles driven, and solve your inequality for $m$.
Answer
\(\boxed{m > 20}\) is the final answer. For mileages greater than 20 miles, company A will charge less than company B.
Step 1 ：David is considering renting a truck for one day from either Company A or Company B. Company A charges a flat rate of $79 with unlimited mileage, while Company B charges an initial fee of $65 and an additional $0.70 for every mile driven.
Step 2 ：We need to find the number of miles for which the cost of renting from company A is less than the cost of renting from company B. This can be represented by the inequality \(79 < 65 + 0.7m\), where \(m\) represents the number of miles driven.
Step 3 ：Solving the inequality for \(m\), we get \(m > 20.0\).
Step 4 ：This means that for any mileage greater than 20 miles, company A will charge less than company B. Therefore, David should choose company A if he plans to drive more than 20 miles.
Step 5 ：\(\boxed{m > 20}\) is the final answer. For mileages greater than 20 miles, company A will charge less than company B.
