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.
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Here's the breakdown for Question 2: Question 2.1 The break-even point is the point at which total costs and total revenue are equal, meaning there is no net loss or gain. In other words, it's the point where a business has covered all its expenses but has not yet made a profit. Question 2.2 Step 1: Calculate total revenue The selling price per apple is R3.00. They sold 116 apples. Total Revenue = Number of apples sold × Selling price per apple Total Revenue = 116 × R3.00 = R348.00 Step 2: Calculate profit The cost of the crate of 116 apples is R255.00. Profit = Total Revenue - Cost of crate Profit = R348.00 - R255.00 Profit = R93.00 Question 2.3.1 Step 1: Calculate profit per apple The cost per apple from the crate is R255.00116. Profit per apple = Selling price per apple - Cost per apple Profit per apple = R3.00 - R255.00116 Profit per apple = R3.00 - R2.19827... Profit per apple ≈ R0.80172... Step 2: Calculate apples sold for R120 profit Let x be the number of apples sold. Total Profit = Profit per apple × x R120 = (R3.00 - R255.00116) × x R120 = ((3 × 116 - 255)/(116)) × x R120 = ((348 - 255)/(116)) × x R120 = (93)/(116) × x x = (120 × 116)/(93) x = (13920)/(93) x = 150 apples Question 2.3.2 Step 1: Determine the break-even point To break even, the total revenue must equal the total cost of the crate. Total Revenue = Cost of crate Selling price per apple × Number of apples = R255.00 R3.00 × Number of apples = R255.00 Step 2: Calculate the number of apples to break even Number of apples = R255.00R3.00 Number of apples = 85 apples Question 2.3.3 Step 1: Identify total amount needed and daily profit The total amount to raise is R13 500.00. The profit per day is R120 (from the premise of Question 2.3). Step 2: Calculate the number of days Number of days = Total amount to raiseProfit per day Number of days = R13\,500.00R120.00/day Number of days = 112.5 days Question 2.4 Step 1: Calculate value for A (Cost for Avis Car Hire for 20 km) Avis Car Hire costs R6.50 per kilometer. A = 20 km × R6.50/km A = R130 Step 2: Calculate value for B (Cost for Budget Car Hire for 40 km) Budget Car Hire costs R165 plus R3.50 per kilometer. B = R165 + (40 km × R3.50/km) B = R165 + R140 B = R305 Step 3: Calculate value for C (Kilometres travelled for given costs) For Avis Car Hire, the cost is R455. C = R455R6.50/km C = 70 km For Budget Car Hire, the cost is R410. R410 = R165 + (C × R3.50/km) R410 - R165 = C × R3.50/km R245 = C × R3.50/km C = R245R3.50/km C = 70 km The completed table is: |l|c|c|c|c| Kilometres travelled & 10 & 20 & 40 & 70 \\ Cost for Avis Car Hire & R65 & R130 & R260 & R455 \\ Cost for Budget Car Hire & R200 & R235 & R305 & R410 \\ That's 2 down. 3 left today — send the next one.