Question

Kyra observed that 85% of the students at the library like to read mystery stories. If 30 students at the library did not like reading mystery stories, the number of students at the library who like mystery stories was _____. (Only numeric values, no other symbols)

Answer 1

Set this up as a proportion. If 85% of students like to read mysteries, that means that 15% don't. Therefore, if 30 students don't like mysteries, then 30 students account for 15% of the total number of students.  Set it up as a ratio where 30 students = 15% and  X students = 85%. Of course in order to use percentages in an equation we have to change them to decimals, .15 and .85 respectively. Then set up the ratio keeping the number of students in alignment and then the percentage of students in alignment (cuz % is not the same as the number of students.)  Like this:
$\frac{students}{percent}: \frac{30}{.15} = \frac{x}{.85}$
Now we cross-multiply to get .15x = 25.5 and x = 170.  That means that 170 students like to read mysteries and that also means that 170 accounts for 85% of the total number of students (which is 200).