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 the total net salary. Let Agnes's net salary be S. Step 2: Calculate the amount spent on rent. Rent = (1)/(10) of S = (1)/(10)S. Step 3: Calculate the remaining amount after paying rent. Remaining amount after rent = S - (1)/(10)S = (9)/(10)S. Step 4: Calculate the down payment for the plot. The down payment was (1)/(2) of the remaining amount. Down payment = (1)/(2) × ((9)/(10)S) = (9)/(20)S. Step 5: Calculate the amount remaining after the down payment. Amount remaining after down payment = (9)/(10)S - (9)/(20)S = (18)/(20)S - (9)/(20)S = (9)/(20)S. Step 6: Set up an equation for the remaining expenses and savings. The amount remaining after the down payment was used for: • Giving mother: sh. 2500 • Shopping: sh. 7500 • Savings: sh. 12,500 The sum of these amounts equals the amount remaining after the down payment. (9)/(20)S = 2500 + 7500 + 12500 (9)/(20)S = 22500 Step 7: Solve for Agnes's net salary, S. S = (22500 × 20)/(9) S = 2500 × 20 S = 50000 Agnes's net salary is sh. 50,000. Step 8: Calculate the down payment. Down payment = (9)/(20)S Down payment = (9)/(20) × 50000 Down payment = 9 × 2500 Down payment = 22500 The down payment Agnes made was sh. 22,500. The final answer is sh. 22,500.