# Ms. Burger has graded 45 tests. This represents 60% of her 3 math classes. How many math students does Ms. Burger teach?

Dec 26, 2016

$75$ students.

We assume that the $45$ tests graded only account for 60% of her students (i.e. only 60% of them on average showed up to class on test day!).

So, we have the equation:

$0.60 s = 45$

where $s$ is the total number of students, so that "$0.60 s$" conveys the phrase, "60% of [the] 3 math classes" and sets that equal to the number of tests graded, $45$.

Note that 60% is also representable in decimal form as $0.60$, since percent means "out of 100".

That means the total number of students (not distinguishing between the number of students per class) is:

$\textcolor{b l u e}{s} = \frac{45}{0.60} = \textcolor{b l u e}{75}$
(we divided both sides by $0.60$)

NOTE: A common mistake is to write:

$s = 0.60 \times 45$,

which is backwards. It would say that there were more tests given out than students who took the test. Make sure your answer makes physical sense.