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.