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: a) Step 1: Determine the time taken by each barber to cut one student's hair. Simon: 20 minutes Tom: 25 minutes John: 30 minutes Step 2: Find the Least Common Multiple (LCM) of the times taken by each barber to find when they will all finish a haircut at the same time, indicating their first break together. Prime factorization: 20 = 2^2 × 5 25 = 5^2 30 = 2 × 3 × 5 LCM (20, 25, 30) = 2^2 × 3 × 5^2 = 4 × 3 × 25 = 300 minutes. Step 3: Convert the total minutes to hours and minutes. 300 minutes = (300)/(60) hours = 5 hours Step 4: Add this duration to the starting time to find the time of their first break. Starting time: 7:30 AM Time of break: 7:30 AM + 5 hours = 12:30 PM. The barbers will first get a break together at 12:30 PM. b) Step 1: Calculate the number of students each barber will have trimmed by the time of their first break (after 300 minutes). Number of students trimmed by Simon = 300 minutes20 minutes/student = 15 students. Number of students trimmed by Tom = 300 minutes25 minutes/student = 12 students. Number of students trimmed by John = 300 minutes30 minutes/student = 10 students. Step 2: Calculate the total number of students trimmed by all barbers. Total students trimmed = 15 + 12 + 10 = 37 students. The total number of students they will have finished to trim by then is 37 students. That's 2 down. 3 left today — send the next one.