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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Dr. Patrick, a pediatrician, has annual checkups and sick visits scheduled next Tuesday, which will fill a total of minutes on her schedule. Next Wednesday, she has annual checkups and sick visit 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.
Full solution
Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Dr. Patrick, a pediatrician, has annual checkups and sick visits scheduled next Tuesday, which will fill a total of minutes on her schedule. Next Wednesday, she has annual checkups and sick visit 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 variables: Define the variables for the types of appointments.Let be the time allotted for an annual checkup.Let be the time allotted for a sick visit.
- Write equations: Write the system of equations based on the given information.For Tuesday: annual checkups and sick visits take minutes.For Wednesday: annual checkups and sick visit take minutes.This gives us the system:
- Multiply and align coefficients: Multiply the second equation by to align the coefficients of for elimination.
- Eliminate variable: Subtract the second equation from the first equation to eliminate .
- Solve for x: Solve for x.Multiply both sides by to get the value of x.
- Substitute into equation: Substitute the value of into the second original equation to solve for .
- Solve for y: Subtract from both sides to solve for .
- Verify solution: Verify the solution by substituting and into both original equations.First equation: Second equation: Both equations are true, so the solution is correct.
