One Friday night, two large groups of people called Weston Taxi Service. The first group requested 2 sedans and 1 minivan, which can seat a

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One Friday night, two large groups of people called Weston Taxi Service. The first group requested 2 sedans and 1 minivan, which can seat a total of 14 people. The second group asked for 2 sedans and 2 minivans, which can seat a total of 20 people. How many passengers can each type of taxi seat? Write a system equation of the this.

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  1. Answer:

    Sedan: 4 passengers

    Minivan: 6 passengers

    Step-by-step explanation:

    We can write the following system of equations:

    [tex]\begin{cases}2s+1m=14 \\2s+2m=20\end{cases}[/tex], where [tex]s[/tex] represents the number of people a sedan can seat and [tex]m[/tex] represents the number of people a minivan can seat.

    Subtracting the first equation from the second, we have:

    [tex]2s+2m-(2s+1m)=20-14,\\\\m=6[/tex]

    Now plug in [tex]m=6[/tex] in any of the equations to solve for [tex]s[/tex]:

    [tex]2s+1(6)=14, \\2s=8, \\s=4[/tex]

    Verify that the solution pair [tex](4, 6)[/tex] works:

    [tex]2(4)+1(6)=14\: \checkmark \\2(4)+2(6)=20 \: \checkmark[/tex]

    Therefore, a sedan can hold 4 passengers and a minivan can hold 6 passengers.

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