The number of students in a geometry class is four fifths the number of students in a Spanish class. The total number of students in both classes does not exceed 54. What is the greatest possible number of students in the Spanish class?

Explanation

Number of students in the Spanish class=x Since the number of students in the geometry class is four fifths the number of students in the Spanish class, the number of students in the geometry class =(4/5)x. The total number of students in both classes does not exceed 54, so we can set up the following inequality: x + (4/5)x ≤ 54 Simplifying this inequality, we get: (9/5)x ≤ 54 Multiplying both sides by 5/9, we get: x ≤ 30 So the greatest possible number of students in the Spanish class is 30, which is option A.