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 are the solutions to your questions: 2.2.1 Step 1: Identify the deposit amount and the total course amount. The deposit amount is R45 000. The total amount for the course is R208 300. Step 2: Write the ratio and simplify it to the form 1 : . The ratio of the deposit amount to the total amount is (45000)/(208300). To express this in the form 1 : x, we divide the total amount by the deposit amount: x = (208300)/(45000) = 4.6288 Step 3: Round the value to two decimal places. x ≈ 4.63 The ratio is 1 : 4.63. 2.2.2 Step 1: Identify the total course amount, deposit, and food-preparation module cost from Option A. Total amount for the course = R208 300 Deposit amount = R45 000 Food-preparation module cost = R99 650 Step 2: Calculate the balance owing for the patisserie module. The balance for the patisserie module is the total amount minus the deposit and the food-preparation module cost. Balance = R208\,300 - R45\,000 - R99\,650 Balance = R163\,300 - R99\,650 Balance = R63\,650 The balance owing for the patisserie module is R63\,650. 2.2.3 Step 1: Calculate the total cost for the food-preparation module under Payment Plan 1. Payment Plan 1: 12 months at R9 000 per month. Cost_1 = 12 × R9\,000 = R108\,000 Step 2: Calculate the total cost for the food-preparation module under Payment Plan 2. Payment Plan 2: R51 825 per semester. The food-preparation module is one year, which is 2 semesters (since 1 semester = 6 months). Cost_2 = 2 × R51\,825 = R103\,650 Step 3: Determine the difference between the two payment plans. Difference = Cost_1 - Cost_2 Difference = R108\,000 - R103\,650 Difference = R4\,350 The difference between payment plan 1 and payment plan 2 for the food-preparation module is R4\,350. 2.2.4 Step 1: Calculate the amount after the first year. Initial investment (P) = R39 500 Interest rate for the first year (i_1) = 7.15% = 0.0715 Amount after 1st year (A_1) = P(1 + i_1) A_1 = R39\,500(1 + 0.0715) A_1 = R39\,500(1.0715) A_1 = R42\,324.25 Step 2: Calculate the amount after the second year. The amount from the first year becomes the new principal for the second year. Interest rate for the second year (i_2) = 7.85% = 0.0785 Amount after 2nd year (A_2) = A_1(1 + i_2) A_2 = R42\,324.25(1 + 0.0785) A_2 = R42\,324.25(1.0785) A_2 = R45\,640.408125 Step 3: Round the final amount to two decimal places. A_2 ≈ R45\,640.41 The total amount that she will receive at the end of the two years is R45\,640.41. Drop the next question! 📸