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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineDr. Yamamoto, a pediatrician, has 33 annual checkups and 11 sick visit scheduled next Tuesday, which will fill a total of 159159 minutes on his schedule. Next Wednesday, he has 11 annual checkup and 11 sick visit on the schedule, which should take 6363 minutes. How much time is allotted for each type of appointment?\newlineThe 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.\newlineDr. Yamamoto, a pediatrician, has 33 annual checkups and 11 sick visit scheduled next Tuesday, which will fill a total of 159159 minutes on his schedule. Next Wednesday, he has 11 annual checkup and 11 sick visit on the schedule, which should take 6363 minutes. How much time is allotted for each type of appointment?\newlineThe time allotted is _\_ minutes for an annual checkup and _\_ minutes for a sick visit.
  1. Define Time Variables: Let's denote the time for an annual checkup as xx minutes and the time for a sick visit as yy minutes.\newlineDr. Yamamoto has 33 annual checkups and 11 sick visit scheduled next Tuesday, which will fill a total of 159159 minutes on his schedule. This can be represented by the equation:\newline3x+y=1593x + y = 159
  2. Schedule for Next Tuesday: Next Wednesday, he has 11 annual checkup and 11 sick visit on the schedule, which should take 6363 minutes. This can be represented by the equation:\newlinex+y=63x + y = 63
  3. Schedule for Next Wednesday: We now have a system of equations:\newline3x+y=1593x + y = 159\newlinex+y=63x + y = 63\newlineWe 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 yy.\newline(3x+y)−(x+y)=159−63(3x + y) - (x + y) = 159 - 63
  4. System of Equations: Perform the subtraction to solve for xx.3x+y−x−y=159−633x + y - x - y = 159 - 632x=962x = 96x=962x = \frac{96}{2}x=48x = 48
  5. Elimination Method: Now that we have the value for xx, we can substitute it back into one of the original equations to solve for yy. Let's use the second equation:\newlinex+y=63x + y = 63\newline48+y=6348 + y = 63\newliney=63−48y = 63 - 48\newliney=15y = 15
  6. Solve for x: We have found the values for xx and yy:x=48x = 48y=15y = 15This means that the time allotted for an annual checkup is 4848 minutes and the time for a sick visit is 1515 minutes.

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