Subjects quantitative techniques

Student Enrollment

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Student Enrollment


1. **Problem 109:** Find the number of students in the Middle Division. Given total students = 2000 Middle Division percentage = 35% = 0.35 Formula: Number of students = Total students \times Percentage Calculation: $$2000 \times 0.35 = 700$$ Answer: 700 students. 2. **Problem 110:** Which division has the largest number of girls? Calculate girls in each division: - Primary Division: 40% of 2000 = 800 students, girls = 50% of 800 = 400 - Middle Division: 35% of 2000 = 700 students, girls = 52% of 700 = 364 - Senior Division: 25% of 2000 = 500 students, girls = 45% of 500 = 225 Largest number of girls is in Primary Division with 400 girls. 3. **Problem 111:** Total student count after 2 years with 5% annual growth. Formula for compound growth: $$P = P_0 (1 + r)^t$$ where $P_0=2000$, $r=0.05$, $t=2$ Calculation: $$2000 \times (1.05)^2 = 2000 \times 1.1025 = 2205$$ Answer: 2205 students. 4. **Problem 112:** Number of Senior Division students not enrolled in STEM Lab. Senior Division students = 25% of 2000 = 500 STEM enrollment = 15% of 500 = 75 Not enrolled = 500 - 75 = 425 Answer: 425 students. 5. **Problem 113:** Difference in number of boys between Primary and Senior Divisions. Primary boys = 50% of 800 = 400 Senior boys = 55% of 500 = 275 Difference: $$400 - 275 = 125$$ Answer: 125 boys. 6. **Problem 114:** New percentage of Middle Division after increasing by 20 students. New Middle Division students = 700 + 20 = 720 Total students = 2000 + 20 = 2020 Percentage: $$\frac{720}{2020} \times 100 = 35.64\% \approx 36.0\%$$ Answer: 36.0%.