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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Dr. Yamamoto, a pediatrician, has $3$ annual checkups and $1$ sick visit scheduled next Tuesday, which will fill a total of $159$ minutes on his schedule. Next Wednesday, he has $1$ annual checkup and $1$ sick visit on the schedule, which should take $63$ minutes. How much time is allotted for each type of appointment? $\newline$ The time allotted is $\_$ minutes for an annual checkup and $\_$ minutes for a sick visit.

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Dr. Yamamoto, a pediatrician, has

3

annual checkups and

1

sick visit scheduled next Tuesday, which will fill a total of

159

minutes on his schedule. Next Wednesday, he has

1

annual checkup and

1

sick visit on the schedule, which should take

63

minutes. How much time is allotted for each type of appointment?

\newline

The time allotted is

\_

minutes for an annual checkup and

\_

minutes for a sick visit.

Define Time Variables: Let's denote the time for an annual checkup as $x$ minutes and the time for a sick visit as $y$ minutes. $\newline$ Dr. Yamamoto has $3$ annual checkups and $1$ sick visit scheduled next Tuesday, which will fill a total of $159$ minutes on his schedule. This can be represented by the equation: $\newline$ $3x + y = 159$
Schedule for Next Tuesday: Next Wednesday, he has $1$ annual checkup and $1$ sick visit on the schedule, which should take $63$ minutes. This can be represented by the equation: $\newline$ $x + y = 63$
Schedule for Next Wednesday: We now have a system of equations: $\newline$ $3x + y = 159$ $\newline$ $x + y = 63$ $\newline$ We can use either substitution or elimination to solve this system. Let's use the elimination method by subtracting the second equation from the first to eliminate $y$ . $\newline$ $(3x + y) - (x + y) = 159 - 63$
System of Equations: Perform the subtraction to solve for $x$ . $3x + y - x - y = 159 - 63$ $2x = 96$ $x = \frac{96}{2}$ $x = 48$
Elimination Method: Now that we have the value for $x$ , we can substitute it back into one of the original equations to solve for $y$ . Let's use the second equation: $\newline$ $x + y = 63$ $\newline$ $48 + y = 63$ $\newline$ $y = 63 - 48$ $\newline$ $y = 15$
Solve for x: We have found the values for $x$ and $y$ : $x = 48$ $y = 15$ This means that the time allotted for an annual checkup is $48$ minutes and the time for a sick visit is $15$ minutes.

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