Of the 180 students in a college course, $\frac{1}{4}$ of the students earned an A for the course, $\frac{1}{3}$ of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?
A. 75
B. 90
C. 105
D. 120
E. 135

Question

Of the 180 students in a college course, $\frac{1}{4}$ of the students earned an A for the course, $\frac{1}{3}$ of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course? 
A. 75 
B. 90 
C. 105 
D. 120 
E. 135

GinnyAnswer · Answer

Calculate the number of students who earned an A: 4 1 ​ × 180 = 45 . 
 Calculate the number of students who earned a B: 3 1 ​ × 180 = 60 . 
 Calculate the number of students who earned a C by subtracting the number of A and B students from the total: 180 − 45 − 60 = 75 . 
 The number of students who earned a C is 75 ​ . 
 
 Explanation 
 
 Understanding the Problem We are given that there are 180 students in a college course. We know the fraction of students who earned an A and the fraction who earned a B. We need to find the number of students who earned a C. 
 
 Calculating the Number of Students with A First, let's find the number of students who earned an A. We are given that 4 1 ​ of the students earned an A. So, we calculate 4 1 ​ × 180 . 
 
 Number of Students with A The result of the calculation is 45. So, 45 students earned an A. 
 
 Calculating the Number of Students with B Next, let's find the number of students who earned a B. We are given that 3 1 ​ of the students earned a B. So, we calculate 3 1 ​ × 180 . 
 
 Number of Students with B The result of the calculation is 60. So, 60 students earned a B. 
 
 Calculating the Number of Students with C Now, we need to find the number of students who earned a C. We know that the rest of the students earned a C. So, we subtract the number of students who earned an A and the number of students who earned a B from the total number of students. That is, 180 − 45 − 60 . 
 
 Number of Students with C The result of the calculation is 75. So, 75 students earned a C. 
 
 Final Answer Therefore, the number of students who earned a C for the course is 75.

Examples 
 Imagine you're planning a school event and need to allocate resources based on student performance. Knowing the distribution of grades (A, B, C) helps you understand the academic standing of the students. If you know the fractions of students achieving A and B grades, you can determine how many students need additional support (those with C grades). This helps in planning tutoring sessions or workshops to improve overall academic performance. Understanding these distributions allows for better resource allocation and targeted support.

Of the 180 students in a college course, $\frac{1}{4}$ of the students earned an A for the course, $\frac{1}{3}$ of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course? A. 75 B. 90 C. 105 D. 120 E. 135

Answer (1)

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Of the 180 students in a college course, $\frac{1}{4}$ of the students earned an A for the course, $\frac{1}{3}$ of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?
A. 75
B. 90
C. 105
D. 120
E. 135