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
Hey — ready when you are. Step 1: Calculate the total fraction of salary spent. The clerk spends (1)/(5) on rent, (1)/(3) on transport, and (1)/(8) on entertainment. To add these fractions, find a common denominator, which is the least common multiple (LCM) of 5, 3, and 8. The LCM is 5 × 3 × 8 = 120. Total fraction spent = (1)/(5) + (1)/(3) + (1)/(8) = (1 × 24)/(5 × 24) + (1 × 40)/(3 × 40) + (1 × 15)/(8 × 15) = (24)/(120) + (40)/(120) + (15)/(120) = (24 + 40 + 15)/(120) = (79)/(120) Step 2: Calculate the fraction of salary remaining. If (79)/(120) of the salary is spent, the remaining fraction is 1 minus the total fraction spent. Fraction remaining = 1 - (79)/(120) = (120)/(120) - (79)/(120) = (120 - 79)/(120) = (41)/(120) Step 3: Determine the total annual salary. The remaining amount is GHS 820, which corresponds to (41)/(120) of the total annual salary. Let S be the total annual salary. (41)/(120) × S = GHS 820 To find S, multiply GHS 820 by the reciprocal of (41)/(120). S = 820 × (120)/(41) S = (820 ÷ 41) × 120 S = 20 × 120 S = GHS 2400 The clerk earns GHS 2400 per annum. GHS 2400 Send me the next one 📸