From the table in the given question, the total number of students that took the test is 64.
Therefore from the table I just constructed, letter "n" represents the total number of students which is 64.
Therefore n= 64.
To solve for x,
The total number of students that studied the test and passed plus the number of students that studied the test and failed= 56.
46+ x= 56
collect like terms
x= 56-46
x= 10.
Therefore the number of students that did the test and failed is represented by x, which is equal to 10 students.
To solve for y,
The total number of students that studied the test and passed plus the number of students that the did not studied the test and passed is equal to 52.
46+ y= 52
collect like term
y= 52-46
y= 6.
Therefore the number of students that did not studied the test and passed
is represented by y, which is equal to 6.
To solve for z,
The total number of students that did not studied the test and passed plus the number of students that did not study and failed the test is equal to 8.
6+z= 8
collect like term
z= 8-6
z= 2