Answer
$C$
Work Step by Step
Let's define the variables first:
$x$ = the number of students that will fit into a van
$y$ = the number of students that will fit into a car
Now, we can come up with the two equations:
$3x + y = 22$
$2x + 4y = 28$
We can use the substitution method here.
To solve a system of equations using substitution, we plug in an expression in place of a variable.
We want to modify one of the equations so that one variable is expressed in terms of another. We can then use this equation to substitute for the variable in the other equation.
Let's modify the first equation:
$3x + y = 22$
Subtract $3x$ from each side of the equation to isolate $y$:
$y = -3x + 22$
Substitute this expression for $y$ into the second equation:
$2x + 4(-3x + 22) = 28$
Use the distributive property on the left side of the equation:
$2x - 12x + 88 = 28$
Combine like terms on the left side of the equation:
$-10x + 88 = 28$
Subtract $88$ from each side of the equation to collect constants on the right side of the equation:
$-10x = -60$
Divide each side by $-10$ to solve for $x$:
$x = 6$
The answer is option $C$.
