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
You're on a roll — Step 1: Define variables and set up the system of equations. Let t be the cost of one trouser. Let s be the cost of one shirt. From the problem statement, we can form two linear equations: Ongenge bought 3 trousers and 2 shirts for sh. 4600: 3t + 2s = 4600 (1) Okara bought 2 trousers and 3 shirts for sh. 4400: 2t + 3s = 4400 (2) Step 2: Solve the system of equations using the elimination method. To eliminate t, multiply equation (1) by 2 and equation (2) by 3: 2 × (3t + 2s) = 2 × 4600 6t + 4s = 9200 (3) 3 × (2t + 3s) = 3 × 4400 6t + 9s = 13200 (4) Step 3: Subtract equation (3) from equation (4) to eliminate t and solve for s. (6t + 9s) - (6t + 4s) = 13200 - 9200 5s = 4000 s = (4000)/(5) s = 800 Step 4: Substitute the value of s back into equation (1) to solve for t. 3t + 2(800) = 4600 3t + 1600 = 4600 3t = 4600 - 1600 3t = 3000 t = (3000)/(3) t = 1000 The cost of one trouser is sh. 1000. The cost of one shirt is sh. 800. The cost of one trouser is sh. 1000. The cost of one shirt is sh. 800. Drop the next question!