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Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineOne Friday night, two large groups of people called Princeton Taxi Service. The first group requested 11 sedan and 22 minivans, which can seat a total of 1515 people. The second group asked for 22 sedans and 33 minivans, which can seat a total of 2424 people. How many passengers can each type of taxi seat?\newlineA sedan can seat _\_ people, and a minivan can seat _\_ people.

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Q. Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.\newlineOne Friday night, two large groups of people called Princeton Taxi Service. The first group requested 11 sedan and 22 minivans, which can seat a total of 1515 people. The second group asked for 22 sedans and 33 minivans, which can seat a total of 2424 people. How many passengers can each type of taxi seat?\newlineA sedan can seat _\_ people, and a minivan can seat _\_ people.
  1. Define Variables: Let's denote the number of people a sedan can seat as ss and the number of people a minivan can seat as mm. The first group's request for 11 sedan and 22 minivans seating a total of 1515 people gives us the equation s+2m=15s + 2m = 15.
  2. Form Equations: The second group's request for 22 sedans and 33 minivans seating a total of 2424 people gives us the equation 2s+3m=242s + 3m = 24.
  3. Eliminate Variable: We now have a system of two equations. We need to eliminate one of the variables, ss or mm. We choose to eliminate ss because its coefficients are 11 and 22, which are easier to work with for elimination.
  4. Multiply and Subtract: To eliminate ss, we multiply the first equation by 22, the coefficient of ss in the second equation. This gives us the new equation 2s+4m=302s + 4m = 30.
  5. Solve for Minivan Capacity: We now subtract the first equation from the new second equation to eliminate ss. This gives us 2s+4m−(2s+3m)=30−242s + 4m - (2s + 3m) = 30 - 24, which simplifies to m=6m = 6.
  6. Calculate Sedan Capacity: We substitute m=6m = 6 into the first equation and solve for ss. This gives us s+2(6)=15s + 2(6) = 15, which simplifies to s+12=15s + 12 = 15 and then s=3s = 3.
  7. Calculate Sedan Capacity: We substitute m=6m = 6 into the first equation and solve for ss. This gives us s+2(6)=15s + 2(6) = 15, which simplifies to s+12=15s + 12 = 15 and then s=3s = 3. Therefore, the cost of each sedan is to seat 33 people and each minivan is to seat 66 people.

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