in a certain math class, each student has a text book, every 2 students share a book of tables, every 3 students share a problem book, and every 4 students share a mathematics dictionary. If the total number of books is 75..

how many students are in a class?
how many students share tables?
how many students share a problem book?
how many students share a math dictionary?

write the equattion
solve the equation
find the solution
answer each question

Let X be the number of students. The total number of books is
X (texts) + X/2 (tables) + X/3 (problem books) + X/4 (dictionaries) =
(1 + 6/12 + 4/12 + 3/12)X = (25/12) X = 75
Solve for X.

To solve the equation (25/12)X = 75, we can multiply both sides of the equation by (12/25) to isolate X:

(12/25) * (25/12)X = (12/25) * 75
X = 36

Therefore, there are 36 students in the class.

To find the number of students who share tables, we can substitute X = 36 into the equation X/2:

36/2 = 18

So, 18 students share tables.

To find the number of students who share a problem book, we can substitute X = 36 into the equation X/3:

36/3 = 12

Hence, 12 students share a problem book.

To find the number of students who share a math dictionary, we can substitute X = 36 into the equation X/4:

36/4 = 9

Therefore, 9 students share a math dictionary.