Finding students with C− but not B− grades

[zorro]

Homework Statement

Five-sixths of the students in class are passing with
a grade of C− or better. Three-fourths of the students
in the same class are passing with a grade of B− or
better. What fraction of the class is not passing with
a grade of B− or better but is passing with a grade of
C− or better?

The Attempt at a Solution

Let 'T' represent the total no. of students in the class.

T = 5T/6 + 3T/4 - x, where x represents the fraction of students passing both with grade B- or better and grade C- or better.
x = 7T/12

So the required fraction = 5T/6 - 7T/12 = T/4 = 0.25 (answer)
This is incorrect. Can someone point out my mistake?

 

[jbunniii]

Let 'T' represent the total no. of students in the class.

T = 5T/6 + 3T/4 - x, where x represents the fraction of students passing both with grade B- or better and grade C- or better.

No, this equation is wrong.

First, "x represents the fraction of students passing both with grade B- or better and grade C- or better" -- isn't that the same as the fraction of students passing with grade B- or better?

Second, these fractions can't add up to all of T. You didn't count the people with grades below C-.

 

[HallsofIvy]

Suppose there are 12 students in the class. "Five-sixths of the students in class are passing with a grade of C− or better." So how many students are passing with a grade of C- or better? "Three-fourths of the students in the same class are passing with a grade of B− or better." So how many students are passing with a grade of B- or better?

Now how many students are passing with a "C" grade? That is, "C- or better" but not "B- or better"? What fraction of the class is that?

(I chose 12 because it is easy to work with- it is divisible by both 6 and 4.)

 

[zorro]

Suppose there are 12 students in the class. "Five-sixths of the students in class are passing with a grade of C− or better." So how many students are passing with a grade of C- or better? "Three-fourths of the students in the same class are passing with a grade of B− or better." So how many students are passing with a grade of B- or better?

Now how many students are passing with a "C" grade? That is, "C- or better" but not "B- or better"? What fraction of the class is that?

(I chose 12 because it is easy to work with- it is divisible by both 6 and 4.)

Ah...I understand it now. It will be 1/12 fraction in both your case and mine. Thanks!