a teacher reported 1/5 made A's, 1/4 made B, 1/3 made C's, 1/6 made D's, and 12 made F's How many are in the class

Let X = the number of students

57/60
+
12
-------

The sum is this:

X = (1/5 + 1/4 + 1/3 + 1/6)*X + 12

X = (57/60)*X + 12

Simplify and solve for X

that's my problem i do not know how to simplify.

To solve for X, we need to add up the fractions representing the different grades and find the common denominator.

First, let's find the common denominator by finding the least common multiple (LCM) of the denominators 5, 4, 3, and 6. The LCM of these numbers is 60.

Now let's convert each fraction to have a denominator of 60:

1/5 = (1/5) * (12/12) = 12/60
1/4 = (1/4) * (15/15) = 15/60
1/3 = (1/3) * (20/20) = 20/60
1/6 = (1/6) * (10/10) = 10/60

Since there are 12 students who received an F, we add that to the sum:

57/60 + 12/60 = 69/60

To simplify the fraction, we divide the numerator and denominator by their greatest common divisor (GCD), which is 3:

69/60 รท 3/3 = 23/20

Now we can set up the equation:

23/20 * X + 12 = X

To solve for X, we can multiply both sides of the equation by the denominator of the fraction (20):

23X + 240 = 20X

Rearranging the equation:

23X - 20X = -240

3X = -240

Dividing both sides by 3:

X = -80

However, the number of students in a class cannot be negative, so this result is not valid. There may be an error in the given information or calculations.