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
Here are the solutions to problems 7, 8, and 9. 7. Step 1: Calculate the cost price per kg of meat. Total cost = Gh¢22.40 Total quantity = 250 kg Cost Price per kg (CP/kg) = Total CostTotal Quantity CP/kg = Gh¢22.40250 kg CP/kg = Gh¢0.0896 per kg Step 2: Calculate the selling price per kg to make a 25% profit. Profit percentage = 25% = 0.25 Selling Price per kg (SP/kg) = CP/kg × (1 + Profit Percentage) SP/kg = Gh¢0.0896 × (1 + 0.25) SP/kg = Gh¢0.0896 × 1.25 SP/kg = Gh¢0.112 He should retail it at Gh¢0.112 per kg. 8. Step 1: Calculate the cost price per kg of tomatoes. Total cost = Gh¢5.20 Total quantity = 130 kg Cost Price per kg (CP/kg) = Gh¢5.20130 kg CP/kg = Gh¢0.04 per kg Step 2: Calculate the selling price and revenue for the first half of the tomatoes. Quantity for first half = 130 kg2 = 65 kg Profit percentage for first half = 30% = 0.30 SP_1 per kg = CP/kg × (1 + 0.30) SP_1 per kg = Gh¢0.04 × 1.30 SP_1 per kg = Gh¢0.052 per kg Revenue from first half = 65 kg × Gh¢0.052 per kg = Gh¢3.38 Step 3: Calculate the quantity for the second half and the amount thrown away. Quantity remaining after first half = 130 kg - 65 kg = 65 kg Quantity thrown away = 5 kg Quantity sold in second half = 65 kg - 5 kg = 60 kg a) Step 4: Calculate the new selling price per kg for the second half. The selling price is reduced by 12% from the previous selling price (SP_1). Reduction percentage = 12% = 0.12 New SP per kg (SP_2) = SP_1 per kg × (1 - 0.12) SP_2 per kg = Gh¢0.052 × 0.88 SP_2 per kg = Gh¢0.04576 per kg The new selling price per kg is Gh¢0.04576. b) Step 5: Calculate the revenue from the second half. Revenue from second half = 60 kg × Gh¢0.04576 per kg = Gh¢2.7456 Step 6: Calculate the total revenue and total profit. Total Revenue = Revenue from first half + Revenue from second half Total Revenue = Gh¢3.38 + Gh¢2.7456 = Gh¢6.1256 Total Cost = Gh¢5.20 Total Profit = Total Revenue - Total Cost Total Profit = Gh¢6.1256 - Gh¢5.20 = Gh¢0.9256 Step 7: Calculate the percentage profit on the whole transaction. Percentage Profit = Total ProfitTotal Cost × 100\% Percentage Profit = Gh¢0.9256Gh¢5.20 × 100\% Percentage Profit ≈ 0.177999 × 100\% Percentage Profit ≈ 17.80\% The percentage profit on the whole transaction is approximately 17.80\%. 9. Step 1: Identify the given values. Cost Price (CP) = Gh¢1200 Selling Price (SP) = Gh¢1680 Step 2: Calculate the profit. Profit = SP - CP Profit = Gh¢1680 - Gh¢1200 Profit = Gh¢480 Step 3: Calculate the profit percentage. Profit Percentage = ProfitCP × 100\% Profit Percentage = Gh¢480Gh¢1200 × 100\% Profit Percentage = (480)/(1200) × 100\% Profit Percentage = 0.4 × 100\% Profit Percentage = 40\% His profit percent is 40\%. 3 done, 2 left today. You're making progress.