Question

a car rental company offers two plans for renting a car: plan a: 30 dollars per day and 19 cents per mile plan b: 50 dollars per day with free unlimited mileage for what range of miles will plan b save you money for a 1 - day rental? to save money the mileage must be greater than miles per day. give your answer accurate to at least one decimal place question help: video post to forum

Explanation:

Step1: Set up cost - functions

Let $x$ be the number of miles driven in a day. The cost of Plan A, $C_A$, is $C_A = 30+0.19x$ (since 19 cents = 0.19 dollars). The cost of Plan B, $C_B$, is $C_B = 50$.

Step2: Set up the inequality

We want to find when Plan B saves money, so we set up the inequality $C_A>C_B$. Substituting the cost - functions, we get $30 + 0.19x>50$.

Step3: Solve the inequality for $x$

Subtract 30 from both sides: $0.19x>50 - 30$. So $0.19x>20$. Then divide both sides by 0.19: $x>\frac{20}{0.19}$.

Step4: Calculate the value of $x$

$x>\frac{20}{0.19}\approx105.3$.

Answer:

$105.3$