Dr. Hoover, a pediatrician, has 3 annual checkups and 2 sick visits scheduled next Tuesday,
which will fill a total of 189 minutes on her schedule. Next Wednesday, she has 3 annual
checkups and 1 sick visit on the schedule, which should take 168 minutes. How much time is
allotted for each type of appointment?
The time allotted is minutes for an annual checkup and minutes for a sick
visit.

Dr. Hoover allot his time on Tuesday for an annual checkup is 147 minutes and for a sick  visit is 42 minutes (Total 189 minutes)

On Wednesday appointment,  he allot his time for an annual checkup is 147 minutes and for a sick  visit is 21  minutes (Total 168 minutes)

solution

Let us assume, minutes for annual checkup denoted as x and

minutes for sick visit denoted as y

The equation of Tuesday visit is      

The equation of Wednesday visit is    

by changing the signs of the equation 2  and  subtract it from the equation 1 we will get   1y = 21 minutes

to substitute y =1 in the equation 2 we get

then now we have substitute both x = 49 and y= 21 in equation ----- 2

we will prove that

so the Tuesday appointment , the time allotted for an annual checkup is 147 minutes and for a sick  visit is 42 minutes (Total 189 minutes)

On Wednesday appointment,  the time allotted for an annual checkup is 147 minutes and for a sick  visit is 21  minutes (Total 168 minutes)