Question

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

Answer 1

`75` students.

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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:

`0.60s = 45`

where `s` is the total number of students, so that "`0.60s`" 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:

`color(blue)(s) = 45/0.60 = color(blue)(75)`
(we divided both sides by `0.60`)

NOTE: A common mistake is to write:

`s = 0.60xx45`,

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.