type your answer in the box. you may use numb...
type your answer in the box. you may use numbers, a decimal point (.), and/or a negative sign (-) in your answer. stella is renting a car for a business trip. the car rental agency charges a flat rate of $60 plus $0.50 per mile for every mile she drives over 40 miles. stellas company will pay up to $270, excluding the cost of gasoline, for the use of the rental car. what is the greatest number of miles stella can drive the rental car without spending more than $270?
Answer
# Explanation:
## Step1: Subtract flat - rate from budget
Let the number of miles driven over 40 miles be $x$. First, subtract the flat rate of $60$ from the total budget of $270$. So the amount available for the miles - based charge is $270 - 60=210$.
## Step2: Set up an equation for miles - based charge
The cost for the miles driven over 40 miles is $0.5x$. We know that $0.5x\leqslant210$. Solving for $x$, we divide both sides of the inequality by $0.5$: $x=\frac{210}{0.5}=420$.
## Step3: Calculate total number of miles
The total number of miles $y$ is the initial 40 miles plus the number of miles driven over 40 miles. So $y = 40+x$. Substituting $x = 420$ into the equation, we get $y=40 + 420=460$.
# Answer:
460