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: Define variables and set up the system of equations. Let x be the school fees for one day scholar. Let y be the charge for one boarder per day. From the problem statement, we can form two linear equations: The total fees for five day scholars and three boarders is sh. 17000: 5x + 3y = 17000 (1) The total fees for three day scholars and two boarders is sh. 11000: 3x + 2y = 11000 (2) Step 2: Solve the system of equations using the elimination method. To eliminate y, multiply equation (1) by 2 and equation (2) by 3: 2 × (5x + 3y) = 2 × 17000 10x + 6y = 34000 (3) 3 × (3x + 2y) = 3 × 11000 9x + 6y = 33000 (4) Step 3: Subtract equation (4) from equation (3) to eliminate y and solve for x. (10x + 6y) - (9x + 6y) = 34000 - 33000 x = 1000 Step 4: Substitute the value of x back into equation (2) to solve for y. 3(1000) + 2y = 11000 3000 + 2y = 11000 2y = 11000 - 3000 2y = 8000 y = 4000 The school fees for each day scholar is sh. 1000. The charge for each boarder is sh. 4000 per day. The school fees for a day scholar is sh. 1000. The charge for a boarder is sh. 4000 per day. Send me the next one 📸