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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 Booneville Taxi Service. The first group requested 22 sedans and 22 minivans, which can seat a total of 1818 people. The second group asked for 33 sedans and 22 minivans, which can seat a total of 2222 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 Booneville Taxi Service. The first group requested 22 sedans and 22 minivans, which can seat a total of 1818 people. The second group asked for 33 sedans and 22 minivans, which can seat a total of 2222 people. How many passengers can each type of taxi seat?\newlineA sedan can seat _____ people, and a minivan can seat _____ people.
  1. Define variables: Define the variables for the number of people each type of taxi can seat.\newlineLet's let SS represent the number of people a sedan can seat, and MM represent the number of people a minivan can seat.
  2. Write equations: Write the system of equations based on the given information.\newlineFor the first group: 2S+2M=182S + 2M = 18 (Equation 11)\newlineFor the second group: 3S+2M=223S + 2M = 22 (Equation 22)
  3. Use elimination method: Use the elimination method to solve the system of equations.\newlineTo eliminate one of the variables, we can multiply Equation 11 by −1.5-1.5 and then add it to Equation 22.\newline−1.5(2S+2M)=−1.5(18)-1.5(2S + 2M) = -1.5(18)\newline−3S−3M=−27-3S - 3M = -27 (Equation 33)\newlineNow add Equation 33 to Equation 22:\newline(3S+2M)+(−3S−3M)=22+(−27)(3S + 2M) + (-3S - 3M) = 22 + (-27)\newline−1M=−5-1M = -5
  4. Solve for M: Solve for M, the number of people a minivan can seat. \newlineM=5M = 5\newlineNow that we know MM, we can substitute it back into one of the original equations to find SS.
  5. Substitute MM for SS: Substitute MM into Equation 11 to find SS.\newline2S+2(5)=182S + 2(5) = 18\newline2S+10=182S + 10 = 18\newline2S=18−102S = 18 - 10\newline2S=82S = 8\newlineS=4S = 4
  6. Check solution: Check the solution by substituting SS and MM into Equation 22.\newline3(4)+2(5)=223(4) + 2(5) = 22\newline12+10=2212 + 10 = 22\newline22=2222 = 22\newlineThe solution checks out.

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