Question

I need help with the following

Answer 1

Let x be the number of miles and y the total cost; therefore, the equations that model the two plans are

`\begin{gathered} PlanA: \\ y_A=30+0.20x \\ PlanB \\ y_B=50 \end{gathered}`

Then, set y_A=y_B as shown below

`\begin{gathered} y_A=y_B \\ \Rightarrow30+0.20x=50 \\ \Rightarrow0.20x=20 \\ \Rightarrow x=(20)/(0.20)=100 \end{gathered}`

Therefore, once the mileage is greater than 100 miles, the total cost of plan B will be less than that of plan A.

The answer is 100 miles.