Write a system of equations to represent the problem and solve by graphing.
10. An art class is planning a trip to a museum. There are 22 people going on the trip. There are four drivers and two types of vehicles, vans and cars. The van can seat six people, while the car can seat four people, including drivers. How many vans and cars does the class need for the trip.

Question

06-01-2022
Mathematics

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Write a system of equations to represent the problem and solve by graphing.
10. An art class is planning a trip to a museum. There are 22 people going on the trip. There are four drivers and two types of vehicles, vans and cars. The van can seat six people, while the car can seat four people, including drivers. How many vans and cars does the class need for the trip.

Sagot :

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facundo3141592 facundo3141592 · Answer 1 · 2022-01-20T06:22:38-05:00

We want to write and solve a system of equations that represents the given situation. We will find that there are 3 vans and 1 car.

How to find the system of equations?

Analyzing the given information we know that:

There are 4 vehicles, we can define the variables:

x = number of vans
y = number of cars.

There is a total of 22 people going in the trip, then we can write the two equations:

x + y = 4

x*6 + y*4 = 22

This is the system of equations, the first one says that there is a total of 4 vehicles and the second says that in these vehicles travel a total of 22 people.

Solving the system of equations:

There are multiple ways of solving it, here we are asked to solve it graphically. To do it, we just need to graph both lines and see where do the lines intercept. The graph of the lines can be seen below.

We can see there that the intercept is at the point (3, 1), meaning that there are 3 vans and 1 car.

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Sagot :

How to find the system of equations?

Solving the system of equations:

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