A taxi ride for the airport to your hotel costs a flat fee of $10 the moment you sit in the back seat plus $0.75 each mile plus a tip of $5 to the driver at the end of the

ride. You want to spend at most $30 to get to your hotel. How many miles away can

your hotel be to meet this condition?

Declare what your variable represents, write the equation or inequality that models

the situation, solve for the variable showing your steps, and answer the question.

3

You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .