Answer:
The complete question seems to be:
A doctor sees between 7 and 12 patients each day.
On Mondays and Tuesdays, the appointment times are 15 minutes.
On Wednesdays and Thursdays, they are 30 minutes.
On Fridays, they are one hour long.
The doctor works for no more than 8 hours a day.
Here are some inequalities that represent this situation.
0.25 ≤ y ≤ 1
7 ≤ x ≤ 12
xy ≤ 8
What represents each variable?
7 ≤ x ≤ 12
We know that the doctor sees between 7 and 12 patients each day, and the smallest value of x is 7, and the largest is 12, then x must represent the number of patients that the doctors see in a given day.
0.25 ≤ y ≤ 1
now,
On Mondays and Tuesdays, each appointment is 15 minutes long.
An hour has 60 minutes.
Then 15 minutes = 15/60 hours = 0.25 hours.
On Wednesdays and Thursdays, they are 30 minutes.
30 minutes = 30/60 hours = 0.5 hours.
Then the possible value of the time for each appointment are {0.25, 0.5, 1}
Then the variable y must represent the time that each appointment takes.
xy ≤ 8
We know that:
x = number of patients in a given day.
y = time that the appointment takes in a given day.
x*y = total number of hours that he works in that given day.
and we know that he works, at maximum, 8 hours.
then the inequality xy ≤ 8 has sense.