Question

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.

Answer 1

Sedan: 4 passengers

Minivan: 6 passengers

Explanation:

We can write the following system of equations:

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

Subtracting the first equation from the second, we have:

`2s+2m-(2s+1m)=20-14,\\\\m=6`

Now plug in
`m=6` in any of the equations to solve for
`s`:

`2s+1(6)=14, \\2s=8, \\s=4`

Verify that the solution pair
`(4, 6)` works:

`2(4)+1(6)=14\: \checkmark \\2(4)+2(6)=20 \: \checkmark`

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