type your answer in the box. you may use numbers, a decimal point (.), and/or a negative sign (-) in your…

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. stella’s 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?

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. stella’s 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: Set up the cost - function

Let $x$ be the number of miles Stella drives. The cost function $C(x)$ has a flat - rate of $60$ and a per - mile charge for miles over $40$. So, $C(x)=60 + 0.5(x - 40)$ for $x\geq40$.

Step2: Set up the inequality

Stella's company will pay up to $270$. So, we set up the inequality $60+0.5(x - 40)\leq270$.

Step3: Simplify the inequality

First, expand the left - hand side: $60+0.5x-20\leq270$. Combine like terms: $40 + 0.5x\leq270$.

Step4: Solve for $x$

Subtract $40$ from both sides: $0.5x\leq270 - 40$, so $0.5x\leq230$. Then divide both sides by $0.5$: $x\leq\frac{230}{0.5}=460$.

Answer:

$460$