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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineTrevor hosts a podcast about computers, and Sharon hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Trevor released 2727 episodes and Sharon released 2727 episodes, for a total of 6,3456,345 minutes of content. This year, Trevor released 3030 episodes and Sharon released 2727 episodes, which lasted a total of 6,5376,537 minutes. How long is each episode?\newlineEach episode of Trevor's podcast is _\_ minutes long, and each episode of Sharon's podcast is _\_ minutes long.

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.\newlineTrevor hosts a podcast about computers, and Sharon hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Trevor released 2727 episodes and Sharon released 2727 episodes, for a total of 6,3456,345 minutes of content. This year, Trevor released 3030 episodes and Sharon released 2727 episodes, which lasted a total of 6,5376,537 minutes. How long is each episode?\newlineEach episode of Trevor's podcast is _\_ minutes long, and each episode of Sharon's podcast is _\_ minutes long.
  1. Equation 11: Let's denote the duration of Trevor's podcast episodes as TT minutes per episode and Sharon's podcast episodes as SS minutes per episode.\newlineWe are given that last year Trevor released 2727 episodes and Sharon also released 2727 episodes for a total of 6,3456,345 minutes of content. This gives us our first equation:\newline27T+27S=6,34527T + 27S = 6,345
  2. Equation 22: This year, Trevor released 3030 episodes and Sharon released 2727 episodes, which lasted a total of 6,5376,537 minutes. This gives us our second equation:\newline30T+27S=6,53730T + 27S = 6,537
  3. Solve System: We now have a system of two equations with two variables:\newline27T+27S=6,34527T + 27S = 6,345\newline30T+27S=6,53730T + 27S = 6,537\newlineTo solve the system, we can subtract the first equation from the second to eliminate SS and solve for TT.\newline(30T+27S)−(27T+27S)=6,537−6,345(30T + 27S) - (27T + 27S) = 6,537 - 6,345\newline30T−27T+27S−27S=6,537−6,34530T - 27T + 27S - 27S = 6,537 - 6,345\newline3T=1923T = 192
  4. Find TT: Divide both sides of the equation by 33 to solve for TT:
    3T3=1923\frac{3T}{3} = \frac{192}{3}
    T=64T = 64
    So, each episode of Trevor's podcast is 6464 minutes long.
  5. Substitute T: Now that we have the value for TT, we can substitute it back into one of the original equations to solve for SS. Let's use the first equation:\newline27T+27S=6,34527T + 27S = 6,345\newline27(64)+27S=6,34527(64) + 27S = 6,345\newline1,728+27S=6,3451,728 + 27S = 6,345
  6. Find S: Subtract 1,7281,728 from both sides of the equation to solve for S:\newline27S=6,345−1,72827S = 6,345 - 1,728\newline27S=4,61727S = 4,617
  7. Find S: Subtract 1,7281,728 from both sides of the equation to solve for SS: \newline27S=6,345−1,72827S = 6,345 - 1,728\newline27S=4,61727S = 4,617Divide both sides of the equation by 2727 to solve for SS: \newline27S27=4,61727\frac{27S}{27} = \frac{4,617}{27}\newlineS=171S = 171\newlineSo, each episode of Sharon's podcast is 171171 minutes long.

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