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In a college philosophy class during the fall semester, there were 323 students. 
42% of the students were philosophy majors, and the rest were not philosophy majors. In the spring semester, the same number of students who were not philosophy majors were in the class as in the fall, but there were only 298 total students in the class. In the spring, what percent of students were not philosophy majors?
Choose 1 answer:
(A) 
46%
(B) 
58%
(c) 
63%
(D) 
92%

In a college philosophy class during the fall semester, there were 323323 students. 42% 42 \% of the students were philosophy majors, and the rest were not philosophy majors. In the spring semester, the same number of students who were not philosophy majors were in the class as in the fall, but there were only 298298 total students in the class. In the spring, what percent of students were not philosophy majors?\newlineChoose 11 answer:\newline(A) 46% 46 \% \newline(B) 58% 58 \% \newline(C) 63% 63 \% \newline(D) 92% 92 \%

Full solution

Q. In a college philosophy class during the fall semester, there were 323323 students. 42% 42 \% of the students were philosophy majors, and the rest were not philosophy majors. In the spring semester, the same number of students who were not philosophy majors were in the class as in the fall, but there were only 298298 total students in the class. In the spring, what percent of students were not philosophy majors?\newlineChoose 11 answer:\newline(A) 46% 46 \% \newline(B) 58% 58 \% \newline(C) 63% 63 \% \newline(D) 92% 92 \%
  1. Calculate Philosophy Majors: Calculate the number of philosophy majors in the fall semester.\newline42%42\% of 323323 students were philosophy majors.\newline0.42×323=135.660.42 \times 323 = 135.66\newlineSince the number of students cannot be a fraction, we round to the nearest whole number.\newline135.66135.66 rounds to 136136 philosophy majors.
  2. Calculate Non-Philosophy Majors (Fall): Calculate the number of students who were not philosophy majors in the fall semester.\newlineTotal students in the fall - Number of philosophy majors == Number of non-philosophy majors\newline323136=187323 - 136 = 187 non-philosophy majors
  3. Determine Non-Philosophy Majors (Spring): Determine the number of non-philosophy majors in the spring semester.\newlineAccording to the problem, the number of non-philosophy majors remains the same in the spring semester as in the fall.\newlineSo, there are 187187 non-philosophy majors in the spring semester.
  4. Calculate Percentage of Non-Philosophy Majors: Calculate the percentage of non-philosophy majors in the spring semester.\newlinePercentage = (Number of non-philosophy majorsTotal number of students in the spring)×100(\frac{\text{Number of non-philosophy majors}}{\text{Total number of students in the spring}}) \times 100\newlinePercentage = (187298)×100(\frac{187}{298}) \times 100
  5. Round Percentage: Perform the calculation to find the percentage.\newlinePercentage = (187298)×10062.75%(\frac{187}{298}) \times 100 \approx 62.75\%\newlineSince we need to choose the closest answer from the options, we round to the nearest whole number.\newline62.75%62.75\% rounds to 63%63\%.