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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 55 sitcoms and 66 dramas, for a total of 341341 minutes of programming, not counting commercials. On Tuesday nights, she has scheduled 11 sitcom and 11 drama, for a total of 6060 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?\newlineSitcoms are _\_ minutes long and dramas are _\_ minutes long.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineA TV station executive is planning the new lineup for next season's shows. On Monday nights, there will be 55 sitcoms and 66 dramas, for a total of 341341 minutes of programming, not counting commercials. On Tuesday nights, she has scheduled 11 sitcom and 11 drama, for a total of 6060 minutes of non-commercial programming. All sitcoms have the same length and all dramas have the same length. How long is each type of show?\newlineSitcoms are _\_ minutes long and dramas are _\_ minutes long.
  1. Define Variables: Let's define the variables: Let s s be the length of a sitcom in minutes, and d d be the length of a drama in minutes.
  2. Write Equations: Write the equations based on the given information: For Monday, 5s+6d=341 5s + 6d = 341 minutes. For Tuesday, s+d=60 s + d = 60 minutes.
  3. Elimination Method: Use the elimination method to solve the system. First, solve the second equation for s s : s=60−d s = 60 - d .
  4. Substitute and Solve: Substitute s=60−d s = 60 - d into the first equation: 5(60−d)+6d=341 5(60 - d) + 6d = 341 .
  5. Simplify and Solve: Simplify and solve for d d : \newline5×60−5d+6d=341300+d=341d=341−300d=41 5 \times 60 - 5d + 6d = 341 \\ 300 + d = 341 \\ d = 341 - 300 \\ d = 41
  6. Find s and d: Substitute d=41 d = 41 back into s=60−d s = 60 - d to find s s :\newlines=60−41s=19 s = 60 - 41 \\ s = 19

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