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 to the questions: 1. Ibrahim spends a quarter of his monthly salary on school fees, one-ninth on water and electricity bills, two thirds of the remainder on house up keep and saves the rest. The difference between what he saves and the amount he spends on house up keep is Kshs. 10,350. Calculate Ibrahim's monthly salary. Step 1: Let Ibrahim's monthly salary be S. Fraction spent on school fees = (1)/(4). Fraction spent on water and electricity bills = (1)/(9). Step 2: Calculate the total fraction spent on fees and bills. Fraction (fees + bills) = (1)/(4) + (1)/(9) = (9)/(36) + (4)/(36) = (13)/(36) Step 3: Calculate the remainder after fees and bills. Remainder = S - (13)/(36)S = (36)/(36)S - (13)/(36)S = (23)/(36)S Step 4: Calculate the amount spent on house upkeep and the amount saved from this remainder. Amount spent on house upkeep = (2)/(3) of the remainder. House upkeep = (2)/(3) × (23)/(36)S = (46)/(108)S = (23)/(54)S Amount saved = (1)/(3) of the remainder. Saved = (1)/(3) × (23)/(36)S = (23)/(108)S Step 5: Use the given difference between house upkeep and savings to find S. The difference is Kshs. 10,350. House upkeep - Saved = 10350 (23)/(54)S - (23)/(108)S = 10350 To subtract, find a common denominator (108). (2 × 23)/(2 × 54)S - (23)/(108)S = 10350 (46)/(108)S - (23)/(108)S = 10350 (23)/(108)S = 10350 Step 6: Solve for S. S = 10350 × (108)/(23) S = 450 × 108 S = 48600 Ibrahim's monthly salary is Kshs. 48,600. 2. Lessons in Lake Primary and Kisumu Girls High Schools take 30 minutes and 40 minutes respectively. The two bells ring simultaneously at 7.50 a.m. How many times will they ring together again between 7.50 a.m. and 3 p.m.? Step 1: Find the least common multiple (LCM) of the ringing intervals. Bell 1 rings every 30 minutes. Bell 2 rings every 40 minutes. Prime factorization: 30 = 2 × 3 × 5 40 = 2^3 × 5 LCM(30, 40) = 2^3 × 3 × 5 = 8 × 3 × 5 = 120 minutes. The bells will ring together every 120 minutes, which is 2 hours. Step 2: Determine the total time duration. Start time: 7:50 a.m. End time: 3:00 p.m. Duration from 7:50 a.m. to 3:00 p.m.: From 7:50 a.m. to 8:00 a.m. = 10 minutes. From 8:00 a.m. to 3:00 p.m. = 7 hours. Total duration = 7 hours and 10 minutes. Convert to minutes: $7 × 60 + 10 = 420 + 10 = 430