Mary is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A has no initial fee but charges 90 cents for every mile driven. Company $B$ charges an initial fee of $\$ 55$ and an additional 70 cents for every mile driven.
For what mileages will Company A charge at least as much as Company B? Use $m$ for the number of miles driven, and solve your inequality for $m$.
Answer
Therefore, for mileages \(m \geq \boxed{275}\), Company A will charge at least as much as Company B.
Step 1 ：Mary is considering renting a truck for one day from either Company A or Company B. Company A charges 90 cents for every mile driven with no initial fee, while Company B charges an initial fee of $55 and an additional 70 cents for every mile driven.
Step 2 ：We need to find the number of miles, denoted as m, for which the cost of renting from Company A is at least as much as the cost of renting from Company B.
Step 3 ：This can be represented by the inequality \(0.90m \geq 55 + 0.70m\).
Step 4 ：Solving this inequality for m gives us \(m \geq 275\).
Step 5 ：This means that when Mary drives 275 miles, the cost of renting from both companies will be the same.
Step 6 ：However, we are interested in the number of miles for which the cost of renting from Company A is at least as much as the cost of renting from Company B.
Step 7 ：Therefore, for mileages \(m \geq \boxed{275}\), Company A will charge at least as much as Company B.
