Problema Solution
A doctors office schedule 10-minute and 20-minute appointments. The doctor also makes hospital rounds for four hours each weekdays. Suppose the doctor limits these activities to, at most, 30 hours per week. A) write a linear inequality to show the number of 10-minute and 20-minute appointments the doctor can schedule. B) what are possible solutions to the problem?
Answer provided by our tutors
Let
x = the number of 10 minute appointments
y = the number of 20 minute appointments
Assuming the doctor work 5 days per week, he spend 4*5 = 20 hours on hospital rounds.
The rest of the time , at most 30 - 20 = 10 hours he spends on appointments.
Since 10 hours = 10*60 min = 600 min we have
10x + 20y <= 600 divide both sides by 10
x + 2y <= 60
The answer for A) is x + 2y <= 60.
B) We know that x and y are positive integers.
We can see the possible solution from the graph of the inequality: x + 2y <= 60
One possible solution is x = 10 and y = 10 that is 10 10-minute and 10 20-minute appointments.