Questions: Bob 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 an initial fee of 47 and an additional 60 cents for every mile driven. Company B charges an initial fee of 35 and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.

Bob 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 an initial fee of 47 and an additional 60 cents for every mile driven. Company B charges an initial fee of 35 and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using m for the number of miles driven.
Transcript text: Bob 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 an initial fee of $\$ 47$ and an additional 60 cents for every mile driven. Company B charges an initial fee of $\$ 35$ and an additional 80 cents for every mile driven. For what mileages will Company A charge no more than Company B? Write your answer as an inequality, using $m$ for the number of miles driven.
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Solution

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Solution Steps

Step 1: Set up the inequality based on the given problem
$A + am < B + bm$ becomes $47 + 0.6m < 35 + 0.8m$.
Step 2: Rearrange the inequality to solve for $m$
$47 - 35 < (0.8 - 0.6)m$
Step 3: Solve for $m$
Since $0.8 - 0.6 > 0$, we find that $m > \frac{47 - 35}{0.8 - 0.6}$.

Final Answer: The number of miles driven must be greater than 60 for Company A to be cheaper.

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