Question

charmaine 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 charges $102 and allows unlimited mileage. company b has an initial fee of $75 and charges an additional $0.90 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.

Explanation:

Step1: Set up the cost - functions

Let $C_A = 102$ be the cost of renting from Company A and $C_B=75 + 0.9m$ be the cost of renting from Company B, where $m$ is the number of miles driven. We want to find when $C_A

Step2: Isolate the variable term

Subtract 75 from both sides of the inequality: $102−75<75 + 0.9m-75$. This simplifies to $27<0.9m$.

Step3: Solve for $m$

Divide both sides of the inequality by 0.9: $\frac{27}{0.9}<\frac{0.9m}{0.9}$. Since $\frac{27}{0.9}=30$, we get $m > 30$.

Answer:

$m>30$