This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions for problems 19c, 20a, 20b, and 20c. Problem 19c: Step 1: Find the total number of parts in the ratio. Total parts = 5 + 4 + 3 = 12 Step 2: Calculate the value of one ratio part by dividing the total amount by the total parts. Value per part = ₦240,00012 = ₦20,000 Step 3: The least share corresponds to the smallest number in the ratio, which is 3. Multiply the value per part by 3. Least share = 3 × ₦20,000 = ₦60,000 The least share is ₦60,000. Problem 20a: Step 1: Find the prime factorization of each number: 9 = 3^2 12 = 2^2 × 3 18 = 2 × 3^2 Step 2: Find the HCF (Highest Common Factor). This is the product of the lowest powers of common prime factors. The only common prime factor is 3, and its lowest power is 3^1. HCF(9, 12, 18) = 3 Step 3: Find the LCM (Least Common Multiple). This is the product of the highest powers of all prime factors present. Highest power of 2 is 2^2. Highest power of 3 is 3^2. LCM(9, 12, 18) = 2^2 × 3^2 = 4 × 9 = 36 Step 4: Find the product of the LCM and HCF: Product = LCM × HCF = 36 × 3 = 108 The product of the LCM and HCF is 108. Problem 20b: Step 1: Identify the given values for simple interest: Principal (P) = ₦30,000.00 Time (T) = 3(1)/(2) years = 3.5 years Rate (R) = 5% per annum = 0.05 Step 2: Use the formula for simple interest: Simple Interest (SI) = (P × R × T)/(100) Step 3: Substitute the values into the formula: SI = (30000 × 5 × 3.5)/(100) Step 4: Perform the multiplication in the numerator: SI = (30000 × 17.5)/(100) SI = (525000)/(100) Step 5: Perform the division: SI = ₦5250.00 The simple interest is ₦5250.00. Problem 20c: Step 1: Calculate the loss amount. Loss = Cost Price - Selling Price Loss = ₦45,000 - ₦30,000 = ₦15,000 Step 2: Calculate the loss percentage using the formula: Loss Percent = LossCost Price × 100\% Step 3: Substitute the values and calculate: Loss Percent = ₦15,000₦45,000 × 100\% Loss Percent = (1)/(3) × 100\% Loss Percent = 33.33\% (to 2 decimal places) The loss percent is 33.33\%. That's 2 down. 3 left today — send the next one.