# Question #2ccd8

Each van carries 18 students and each bus carries 59 students.

#### Explanation:

Let v = the number of students a van carries
Let b = the number of students a bus carries

For the string orchestra, we know that they have 372 students and they filled 1 van and 6 buses, so:

$372 = 1 v + 6 b$ (we'll call this equation 1)

for the bands, we know that they had 390 students and they filled 2 vans and 6 buses, so:

$390 = 2 v + 6 b$ (this can be equation 2)

To solve for one of the variables, let's subtract one equation from the other - either way will work, but in this case, I'm subtracting equation 1 from equation 2 so we don't have to deal with negative numbers.

$390 = 2 v + 6 b$
$- \left(372 = v + 6 b\right)$ gives us:
$\left(390 - 372\right) = \left(2 v - v\right) + \left(6 b - 6 b\right)$
$18 = v$ so each van holds 18 students!

We can now substitute this into either of the original equations and solve for b:

$372 = v + 6 b$
$372 = 18 + 6 b$
$354 = 6 b$
$59 = b$ so each bus holds 59 students!

If you want to check your answer, you can substitute the numbers you got into the equation that you didn't use to solve for the last step:

$390 = 2 \left(18\right) + 6 \left(59\right)$
$390 = 390$
This statement is true, which means our answer is correct!