# There were a total of 107 students and chaperones on a field trip to the museum. If the number of chaperones was thirteen less than seven times the number of students, what is the number of students?

May 9, 2018

There are $92$ chaperones and $15$ students.

#### Explanation:

So I'll set up an equation to help solve this, with $s$ for students and $c$ for chaperones.

$c = 7 s - 13$
$s + c = 107$
$s + \left(7 s - 13\right) = 107$

The bottom equation is essentially saying that students plus chaperones (which equals 13 less than 7 times the number of students) equals 107 people.

You can remove the parentheses from this equation:

$s + 7 s - 13 = 107$

And combine like terms:

$8 s = 120$

And divide both sides by $8$:

$\frac{8 s}{8} = \frac{120}{8}$

To get:

$s = 15$

Because $c = 7 s - 13$, you can plug in $15$ in for $s$ to get:

$c = 7 \left(15\right) - 13$
$c = 105 - 13$
$c = 92$

And to double check:

$92 + 15 = 107$

Meaning that there are $92$ chaperones and $15$ students. Not sure why there are so many chaperones for so few students, but there we are.