How long can students park in the lot?

Question

Parking in a student lot cost $3 for the first 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 that a student can park in this lot for $7?

Answer 1

Students can park in the lot for half an hour for $3. So really, this question comes down to how long students can park in the lot for $7 - $3 = $4 after the first half hour. If we let x = number of hours parked after the first half hour, we want the following equation to be true:

 

$1.75x < $4

x < 2.3

 

After the first half hour, the students could park in the lot for up to x = 2.3 hours for less than $4. However, a partial hour is charged like a full hour. That means we have to round down to the nearest integer, 2 hours.

 

So, after the first half hour, students can park in the lot for at most 2 hours if they want to pay less than $4. Adding in the first half hour, students can park in the lot for at most 2.5 hours if they want to pay less than $7.

 

 

Checking our work, we see that a 2.5 hour stay would cost $3 + 2($1.75) = $3 + $3.50 = $6.50. Any extra time would cost another $1.75, which would put the total cost over $7.