Can someone please explain this qestion and how to solve.
A doctors office schedules 15 min appointments for weekdas. The doctor limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15 min appointments x and the number of half hour appointments y the doctor may have in a week.
y = 2x
x + y ≤ 30
Substitute 2x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
Sorry, the second equation should be as indicated below.
15x + 30y ≤ 30*60
Substitute 2x for y in second equation and solve for x. Insert that value into the first equation and solve for y. Check by inserting both values into the second equation.
To solve this problem, we need to consider the number of 15-minute appointments (x) and the number of half-hour appointments (y) the doctor can have in a week.
Given that each 15-minute appointment takes 1/4 of an hour and each half-hour appointment takes 1/2 of an hour, we can express the total time in hours spent on these appointments.
The doctor's office schedules 15-minute appointments for weekdays, which implies there are 5 weekdays in a week. We can calculate the time spent on 15-minute appointments in a week by multiplying the number of 15-minute appointments (x) by 1/4 and then multiplying it by 5.
Similarly, the time spent on half-hour appointments can be calculated by multiplying the number of half-hour appointments (y) by 1/2 and then multiplying it by 5 since the doctor only works on weekdays.
Therefore, the total time spent on appointments must be less than or equal to 30 hours a week, which can be represented by the inequality:
(1/4)x + (1/2)y ≤ 30
This inequality ensures that the sum of the time spent on 15-minute appointments (in hours) and the time spent on half-hour appointments (in hours) does not exceed 30.