My Apps Dashboard I Gwinnel Content / MATH1111: College Do Homework - Lesson 2-5.1 om/Student/PlayerHomework.aspx?homeworkld=690000007\&questionld=1\&flushed=false\&cld=8139970\&back=https://mylab.pearson.com/St... Leslie Alvarado 02/17/25 10:20 PM 5.1 Solve Systems of Question 12, 5.1.77 HW Score: \( 31.25 \%, 5 \) of 16 points Part 1 of 2 Points: 0 of 1 Save At the north campus of a performing arts school, \( 40 \% \) of the students are music majors. At the south campus, \( 50 \% \) of the students are music majors. The campuses are merged into one east campus. If \( 46 \% \) of the 1500 students at the east campus are music majors, how many students did each of the north and south campuses have before the merger? The north campus had \( \square \) 600900 students.

Let x = number of students in the north campus and y = number of students in the south campus, with x + y = 1500. At the north campus, 40% are music majors, contributing 0.40x majors. At the south campus, 50% are music majors, contributing 0.50y majors. When merged, 46% of the 1500 students are music majors, so there are 0.46 × 1500 = 690 music majors in total. This gives the equation:   0.40x + 0.50y = 690 Substitute y = 1500 – x into the equation:   0.40x + 0.50(1500 – x) = 690 Now solve for x:   0.40x + 750 – 0.50x = 690   (0.40x – 0.50x) + 750 = 690   –0.10x + 750 = 690   –0.10x = 690 – 750   –0.10x = –60   x = –60 / –0.10   x = 600 So, the north campus had 600 students. To check, the south campus had:   y = 1500 – 600 = 900 students. Verifying the counts of music majors:   North: 0.40 × 600 = 240 majors   South: 0.50 × 900 = 450 majors   Total = 240 + 450 = 690 majors, which matches the provided information. Thus, before the merger, the north campus had 600 students and the south campus had 900 students.