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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Dr. Thompson, a pediatrician, has annual checkups and sick visits scheduled next Tuesday, which will fill a total of minutes on his schedule. Next Wednesday, he has annual checkups and sick visits on the schedule, which should take 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.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Dr. Thompson, a pediatrician, has annual checkups and sick visits scheduled next Tuesday, which will fill a total of minutes on his schedule. Next Wednesday, he has annual checkups and sick visits on the schedule, which should take 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.
- Define Equations: Let's denote the time for an annual checkup as minutes and the time for a sick visit as minutes.We need to set up two equations based on the information given.
- Set Up Equations: For next Tuesday, the equation based on the information given is: (time for annual checkups) + (time for sick visits) = minutes.So, we have the equation: .
- Solve for Variables: For next Wednesday, the equation based on the information given is: (time for annual checkups) + (time for sick visits) = minutes.So, we have the equation: .
- Substitute and Solve: We now have a system of equations:We can solve this system using the elimination method by subtracting the first equation from the second to eliminate .
- Final Results: Subtracting the first equation from the second gives us:This simplifies to:
- Final Results: Subtracting the first equation from the second gives us:This simplifies to:Now that we have the value for , we can substitute it back into one of the original equations to solve for . Let's use the first equation:
- Final Results: Subtracting the first equation from the second gives us:This simplifies to:Now that we have the value for , we can substitute it back into one of the original equations to solve for . Let's use the first equation:Simplify and solve for :
- Final Results: Subtracting the first equation from the second gives us:This simplifies to:Now that we have the value for , we can substitute it back into one of the original equations to solve for . Let's use the first equation:Simplify and solve for :We have found the values for and : minutes for an annual checkup minutes for a sick visitThese are the times allotted for each type of appointment.
