SOLUTION: All students in Ms. Fay's Spanish class are either going on the Spain trip, the Mexico trip, or both. 1/4 of the students going to Spain are also going to Mexico, and 2/7 of the st

Let x be the number of students going to the Spain trip;
    y                           going to the Mexico trip;
    z                           going to both trips.


We are given

     = z,

     = z.


or, equivalently,

     x = 4z,
    2y = 7z.


The total is  x + y - z = 4z +  - z = 3z + .

So we should check the appropriate values of z, if they can produce the values of the option's list.


For short, let's make a Table

    T   A   B   L   E
  -----------------------------

    z		3z + (7/2)z
		
    3		19.5
    4		26
    5		32.5
    6		39
    7		45.5
    8		52


Looking in this Table, we see only ONE opportunity for possible solution: 26 students.


ANSWER.  Under given conditions, the only possible solution is 26 students in the class.