In a high school, students have the option to choose two elective courses: Photography and Music. All students in the Art Department are required to take both courses, while students from other departments can select one of the two options. Grades are given based on performance with A, B and C representing different levels of achievement and F for failure. Consider the following additional information about the number of students who took these courses this year and the grades they obtained:(i) The ratio of the number of non-Art Department students who chose Photography to that of those who chose Music was 3 : 4.(ii) The total number of non-Art Department students who took either Photography or Music was equal to the number of Art Department students.(iii) The number of non-Art Department students who failed in both Photography and Music courses was the same, and this total was equivalent to the number of Art Department students who received grade C in Music.(iv) Among the students who passed Music courses, 60% achieved grade B. However, while the numbers of students who received grades A and C were equal for Photography, the ratio for Music was 24 : 7.(v) No Art Department student failed in the Photography course, and no non-Art Department student received grade A in Photography.(vi) The ratio of the numbers of Art Department students who received grades A, B and C in Photography was 3 : 5 : 2, while for Music, the ratio was 4 : 5 : 1.(vii) The ratio of the total number of non-Art Department students failing in either of the two courses to the number of Art Department students failing in either of the two courses was 2 : 1.(viii) A total of 20 students failed in the Music course.Question No. 1What is the number of non-Art Music students who got grade C?8101416
Question
In a high school, students have the option to choose two elective courses: Photography and Music. All students in the Art Department are required to take both courses, while students from other departments can select one of the two options. Grades are given based on performance with A, B and C representing different levels of achievement and F for failure. Consider the following additional information about the number of students who took these courses this year and the grades they obtained:(i) The ratio of the number of non-Art Department students who chose Photography to that of those who chose Music was 3 : 4.(ii) The total number of non-Art Department students who took either Photography or Music was equal to the number of Art Department students.(iii) The number of non-Art Department students who failed in both Photography and Music courses was the same, and this total was equivalent to the number of Art Department students who received grade C in Music.(iv) Among the students who passed Music courses, 60% achieved grade B. However, while the numbers of students who received grades A and C were equal for Photography, the ratio for Music was 24 : 7.(v) No Art Department student failed in the Photography course, and no non-Art Department student received grade A in Photography.(vi) The ratio of the numbers of Art Department students who received grades A, B and C in Photography was 3 : 5 : 2, while for Music, the ratio was 4 : 5 : 1.(vii) The ratio of the total number of non-Art Department students failing in either of the two courses to the number of Art Department students failing in either of the two courses was 2 : 1.(viii) A total of 20 students failed in the Music course.Question No. 1What is the number of non-Art Music students who got grade C?8101416
Solution
The text is written in English, so I will respond in English.
To find the number of non-Art Music students who got grade C, we need to use the information given in the problem.
From point (iv), we know that the ratio of students who received grades A and C in Music was 24 : 7.
From point (viii), we know that a total of 20 students failed in the Music course.
From point (iii), we know that the number of non-Art Department students who failed in both Photography and Music courses was the same, and this total was equivalent to the number of Art Department students who received grade C in Music.
From point (ii), we know that the total number of non-Art Department students who took either Photography or Music was equal to the number of Art Department students.
From point (vi), we know that the ratio of the numbers of Art Department students who received grades A, B and C in Music was 4 : 5 : 1.
From these points, we can set up the following equations:
Let's denote: N = total number of non-Art Department students A = total number of Art Department students F = total number of students who failed (20 students)
From point (ii), we have: N = A
From point (iii), we have: F = number of Art Department students who received grade C in Music
From point (vi), we have: 1/10 * A = F
Solving these equations, we get: A = 10 * F = 10 * 20 = 200 students N = A = 200 students
From point (iv), we have: Number of non-Art Music students who got grade C = 7/31 * (N - F) = 7/31 * (200 - 20) = 7/31 * 180 = 40.32
However, the number of students cannot be a decimal, so we need to round it to the nearest whole number. Therefore, the number of non-Art Music students who got grade C is approximately 40.
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