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: Calculate the school fees after the scholarship discount. The original school fees are shs. 3,000,000. The scholarship offers a 50% discount on school fees. Discount amount = 0.50 × shs. 3,000,000 = shs. 1,500,000 New school fees = shs. 3,000,000 - shs. 1,500,000 = shs. 1,500,000 Step 2: Calculate the boarding fees after the scholarship reduction. The original boarding fees are shs. 1,500,000. The scholarship offers a shs. 200,000 reduction. New boarding fees = shs. 1,500,000 - shs. 200,000 = shs. 1,300,000 Step 3: Calculate the cost of school supplies after the scholarship voucher. The original cost of school supplies is shs. 500,000. The scholarship offers a shs. 150,000 voucher. New school supplies cost = shs. 500,000 - shs. 150,000 = shs. 350,000 Step 4: Calculate the total expenses after applying the scholarship. The total expenses are the sum of the new school fees, new boarding fees, and new school supplies cost. Total expenses = shs. 1,500,000 + shs. 1,300,000 + shs. 350,000 = shs. 3,150,000 The aunt's budget is shs. 5,000,000, so the total expenses are within the budget. Step 5: Detail payment Option 1 for the new school fees. The new school fees are shs. 1,500,000. Option 1 involves two installments: two-fifths at the beginning of the term and the balance before midterm exams. First installment = (2)/(5) × shs. 1,500,000 = 2 × shs. 300,000 = shs. 600,000 Second installment = shs. 1,500,000 - shs. 600,000 = shs. 900,000 Under Option 1, the payments would be shs. 600,000 at the beginning of the term and shs. 900,000 before midterm exams. Step 6: Detail payment Option 2 for the new school fees. The new school fees are shs. 1,500,000. Option 2 involves four equal installments. Amount per installment = shs. 1,500,0004 = shs. 375,000 Under Option 2, four equal payments of shs. 375,000 would be made at the beginning of the term, before midterm exams, after midterm, and before final exams. The total expenses after the scholarship are shs. 3,150,000. That's 2 down. 3 left today — send the next one.