a large group of students want to go to the movies. if the students take 3 vans and 1 car they can transport 22 people. if they take 2 vans and 4 cars. they can transport 28 people.write and solve a system of equations to find the number of people that can be transported in a van. show your work
Question 1
3v + c = 22 (1)
2v + 4c = 28 (2)
From (1)
3v + c = 22
c = 22 - 3v (3)
Substitute (3) into (2)
2v + 4(22 - 3v) = 28
2v + 88 - 12v = 28
-10v = -60
v = 6
Therefore, the number of people that can be transported in a van is 6
To solve this problem, let's assign variables to the number of people that can be transported in a van (let's call it "v") and the number of people that can be transported in a car (let's call it "c").
From the first statement, we know that 3 vans and 1 car can transport 22 people. So we can write the equation:
3v + 1c = 22
From the second statement, we know that 2 vans and 4 cars can transport 28 people. So we can write the second equation:
2v + 4c = 28
Now, we have a system of two equations with two variables. We can solve them using any method of solving systems of equations. In this case, I will use the substitution method.
From the first equation, we can solve for c:
c = 22 - 3v
Now, we substitute this value of c into the second equation and solve for v:
2v + 4(22 - 3v) = 28
2v + 88 - 12v = 28
-10v + 88 = 28
-10v = 28 - 88
-10v = -60
v = -60/-10
v = 6
Therefore, the number of people that can be transported in a van is 6.