Question

a car rental company offers two plans for renting a car. plan a: 20 dollars per day and 10 cents per mile plan b: 40 dollars per day with free unlimited mileage what is the maximum number of miles you can drive so that the total cost of plan a is less than the total cost of plan b? if you drive less than \boxed{} miles, plan a is less expensive.

Explanation:

Step1: Define variables and cost functions

Let \( x \) be the number of miles driven. The cost of Plan A (\( C_A \)) is \( 20 + 0.10x \) dollars (20 dollars per day plus 10 cents per mile, where 10 cents = \( \$0.10 \)). The cost of Plan B (\( C_B \)) is \( 40 \) dollars per day (unlimited mileage).

Step2: Set up the inequality

We want \( C_A < C_B \), so:
\[
20 + 0.10x < 40
\]

Step3: Solve the inequality

Subtract 20 from both sides:
\[
0.10x < 40 - 20
\]
\[
0.10x < 20
\]
Divide both sides by 0.10:
\[
x < \frac{20}{0.10}
\]
\[
x < 200
\]

Answer:

200