Question

SaA group of 41 people are going to а concert together in 7 vehicles. Some of the vehiclescan hold 7 people each, and the rest can hold 5 people each. Assuming all the vehiclesare filled to capacity, exactly how many ofthe vehicles can hold 7 people?

Answer 1

To find out how many vehicles can hold 7 people when 41 people are going to a concert in 7 vehicles, we set up and solve a system of equations.

The solution reveals that 3 vehicles can hold 7 people.

Step-by-step explanation:

Let us solve the problem, which is a classic example of a system of equations scenario, where we have two variables: the number of vehicles that can hold 7 people and the number of vehicles that can hold 5 people.

Given that there are 41 people going to the concert and 7 vehicles in total, some holding 7 people and the rest holding 5, we want to find out exactly how many of the vehicles can hold 7 people.

Let's define our variables.

Let x be the number of vehicles that hold 7 people, and y be the number of vehicles that hold 5 people.

We can set up two equations based on the information provided:

1. Equation 1 (Total number of vehicles): x + y = 7
2. Equation 2 (Total number of people): 7x + 5y = 41

Solving this linear system of equations, we can multiply Equation 1 by 5 to get a new equation that will help us eliminate y by subtraction.

5x + 5y = 35 (Equation 3)

Subtracting Equation 3 from Equation 2 gives us:

2x = 6

Dividing by 2, we find:

x = 3

Therefore, there are 3 vehicles that can hold 7 people.

To find the number of vehicles that hold 5 people, we plug x back into Equation 1:

3 + y = 7

y = 4

So, there are 4 vehicles that can hold 5 people.