Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Dr. Meyer, a pediatrician, has 1 annual checkup and 2 sick visits scheduled next Tuesday, which will fill a total of 91 minutes on his schedule. Next Wednesday, he has 1 annual checkup and 3 sick visits on the schedule, which should take 109 minutes. How much time is allotted for each type of appointment?

Answer 1

• Sick visit: 18 min

,

• Annual checkup: 55 min

Step-by-step explanation

Let x be the time of the annual checkup and y be the time of the sick visit.

On Tuesday, Dr. Meyer has 1 annual checkup and 2 sick visits, which add up a total of 91 minutes: x + 2y = 91.

On Wednesday, he has 1 annual checkup and 3 sick visits, adding a total of 109 minutes: x + 3y = 109.

So we have the following system of equations,

`\begin{cases}x+2y=91 \\ x+3y=109\end{cases}`

We can find the values of the variables using the method of elimination. Subtract the first equation from the second,

The sick visits last 18 minutes. To find the time the annual checkups take, we have to solve one of the equations for x and replace the value of y,

`\begin{gathered} x=91-2y \\ x=91-2\cdot18 \\ x=55 \end{gathered}`

So the annual checkup lasts 55 minutes.