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's the solution for Item 1: Item 1: a) i) At what time will all the barbers first get a break together? Step 1: Identify the time each barber takes for a haircut. Simon: 18 minutes Tom: 25 minutes John: 30 minutes Step 2: Find the Least Common Multiple (LCM) of 18, 25, and 30 to determine when they will all finish a haircut at the same time. Prime factorization: 18 = 2 × 3^2 25 = 5^2 30 = 2 × 3 × 5 The LCM is 2^1 × 3^2 × 5^2 = 2 × 9 × 25 = 450 minutes. Step 3: Convert the total minutes into hours and minutes. 450 minutes = (450)/(60) hours = 7