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
Step 1: Determine John's initial earnings. Let John's initial earnings be J_0. His earnings increased by 12\%, and his new earnings (J_new) are Sh. 5600. J_new = J_0 × (1 + 0.12) 5600 = J_0 × 1.12 J_0 = (5600)/(1.12) J_0 = 5000 Sh. Step 2: Determine Musa's initial earnings. The ratio of John's initial earnings to Musa's initial earnings (M_0) is 5:3. (J_0)/(M_0) = (5)/(3) Substitute J_0 = 5000: (5000)/(M_0) = (5)/(3) 5 M_0 = 5000 × 3 5 M_0 = 15000 M_0 = (15000)/(5) M_0 = 3000 Sh. Step 3: Determine Musa's new earnings. The sum of their new earnings is Sh. 9600. We know John's new earnings (J_new) are Sh. 5600. Let Musa's new earnings be M_new. J_new + M_new = 9600 5600 + M_new = 9600 M_new = 9600 - 5600 M_new = 4000 Sh. Step 4: Calculate the percentage change in Musa's earnings. The percentage change is calculated as New earnings - Initial earningsInitial earnings × 100\%. Percentage change = M_new - M_0M_0 × 100\% Percentage change = (4000 - 3000)/(3000) × 100\% Percentage change = (1000)/(3000) × 100\% Percentage change = (1)/(3) × 100\% Percentage change = 33(1)/(3)\% Percentage change ≈ 33.33\% The percentage change in Musa's earnings is: 33(1)/(3)\% or 33.33\% 3 done, 2 left today. You're making progress.