Parking in a student lot cots $1 for the frist half hour and $1.75 for each hour thereafter. A partial hour is charged the same as a full hour. What is the longest time a student can park in this lot for $10?

Question

anonymous · Answer

There are some typos please I aplogize

anonymous · Answer

Does anyone know how to do this one? I some what know, that you have to divide the number of hours by the amount which is; 9/1.75, right?

anonymous · Answer

Well, I got the answer, but I did it by trial and error, which is not the way you want.  Still trying.

anonymous · Answer

Okay

anonymous · Answer

Okay I got it, the student is already out of $1, so $9 is left, in 5hrs he has spent $8.75,

anonymous · Answer

It's a "ceiling" or "greatest integer" question.  The first half-hour costs $1, so you get that 1/2 hour as time toward your max.  You then add to that the "greatest integer" whereby:   [(7/4)x] <= 9   where the [] here means greatest integer.  We get [x] <= 36/7 and therefore [x] is 5 because 5 is the greatest integer that is still less than 36/7.  So, your final answer is 5 and a half because you had that first half-hour.  We should probably talk about this one a little.

anonymous · Answer

Yes, your trial-and-error method was what I did.  I followed it up with the greatest integer math.

anonymous · Answer

Thank you for your help.

anonymous · Answer

It's actually a tough little problem!  you're welcome!