Calculate the number of girls next year and advise the head teacher on saving funds for a new dormitory.

You're on a roll — Here are the solutions for Item 5: Part 1: Head teacher's decision on girls' dormitory Step 1: Calculate the total student population for next year. Current student population = 500. Annual increase rate = 8\%. Increase in students = 0.08 × 500 = 40 students. Total student population next year = 500 + 40 = 540 students. Step 2: Determine the number of girls next year. The ratio of boys to girls is 4:5. Total parts in the ratio = 4 + 5 = 9. Number of girls next year = (5)/(9) × 540 = 5 × 60 = 300 girls. Step 3: Advise the head teacher on saving funds. The head teacher plans to build a new girls' dormitory if the number of girls will exceed 250. Since 300 > 250, the number of girls next year will indeed exceed 250. Therefore, the head teacher should be certain to start saving funds now for the new girls' dormitory. Part 2: Cost of transporting construction materials Step 1: Find the greatest common divisor (GCD) of the quantities of materials. The quantities of materials are: 360 bags of cement, 240 kg of binding wire, and 300 steel rods. To ensure each trip carries equal quantities of each item with no remainder, the number of trips must be a common divisor of these quantities. To minimize the number of trips (and thus the cost), we find the Greatest Common Divisor (GCD). Prime factorization of the quantities: 360 = 2^3 × 3^2 × 5^1 240 = 2^4 × 3^1 × 5^1 300 = 2^2 × 3^1 × 5^2 The GCD is found by taking the lowest power of each common prime factor: GCD(360, 240, 300) = 2^(3,4,2) × 3^(2,1,1) × 5^(1,1,2) GCD = 2^2 × 3^1 × 5^1 = 4 × 3 × 5 = 60 Step 2: Determine the number of trips required. The number of trips required is equal to the GCD of the quantities. Number of trips = 60. Step 3: Calculate the total cost of transportation. Cost per trip = Shs 55,000. Total cost of transportation = Number of trips × Cost per trip Total cost = 60 × Shs 55,000 = Shs 3,300,000. The