Question

Christian randomly selects students from his grade to rate a math test as easy, moderate, or difficult. Of the students he surveyed, 13 said the test was easy, 11 rated it as moderate, and 3 found it difficult. Assuming that all students took the same test, how many of the 162 total students in Christian’s grade would probably rate the test something other than easy?

Answer 1

13 students rated the test as easy
11 students rated the test as moderate
3 students rated the test as difficult

So how many students did he survey in all?
How many of the students that he surveyed said that the test was something other than easy? (That is, they said it was moderate or difficult.)

Finally we set up a proportion to solve your question.
We call 'x' the number of students who would probably rate the test as something other than easy.

\( \frac{\text{# of students surveyed who found the test moderate or difficult}}{\text{total students surveyed}} = \frac{x}{\text{total # of students who took the test}}\)

And remember, one way to solve proportions is
\(\Large \frac{a}{b}=\frac{c}{d} ~~~~ \Rightarrow ad = bc\)

And then you simply isolate the variable you're solving for.