How do you find the range of a word problem?

Question

1. Lesley is a math and science tutor. She offers tutoring sessions that are  hours long. The equation represents her charge in dollars for a math session that is h hours long. For science, she charges the same one-time fee but a different hourly rate. She charges $105 for a 3-hour science tutoring session.
2. Write an equation in slope-intercept form that represents the total charge, s, of a science tutoring session that is h hours long. 
3. Find the reasonable range for both the math and science tutoring session equations. 

Answer 1

Remember that the range is the bounds of the output, in this case the total charge for a tutoring session.

Now, since it's up to you to determine a reasonable range, we have options. Since it asks about a session, the minimum is one hour plus the fee, but the argument could be made that it's either 0 upon cancellation or the one-time fee if the session is cancelled within 24 hours.

As far as the maximum, what's a reasonable max time for a session? Don't forget to add the fee!

Answer 2

In a word problem, you just need to identify which variable is independent and which is dependent.

The range will be the minimum and maximum values of the dependent variable.

For this question, tutoring sessions are certain lengths of time, h hours long.

The "h" hours is the independent variable.

The amount of money she earns is the dependent variable.

So, the range will be between these two numbers:

1) the minimum she can possibly earn from the shortest possible tutoring session

2) the maximum she can possible earn from the longest possible tutoring session

I don't see enough info to solve the problem for you, but this should answer how to find the range of a word problem. Hope this helps! :)