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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Step 1: Answer question 1.2.1. To calculate the total expenses, we use the formula: Total Expenses = (Cost per brochure × Number of brochures) + Fixed machine hire. The cost per brochure is R10, and the fixed machine hire is R1000. For A, the number of brochures is 100. A = (10 × 100) + 1000 A = 1000 + 1000 A = 2000 For B, the number of brochures is 200. B = (10 × 200) + 1000 B = 2000 + 1000 B = 3000 Value A = R2000 Value B = R3000 Step 2: Answer question 1.2.2. Let E be the total expenses and x be the number of brochures printed. The cost per brochure is R10 and the fixed machine hire is R1000. E = 10x + 1000 E = 10x + 1000 Step 3: Answer question 1.2.3. To calculate the total income, we use the formula: Total Income = (Charge per brochure × Number of brochures). Solly charges R20 per brochure. For C, the number of brochures is 100. C = 20 × 100 C = 2000 For D, the number of brochures is 200. D = 20 × 200 D = 4000 Value C = R2000 Value D = R4000 Step 4: Answer question 1.2.4. This question requires drawing a graph. I will provide the points for the income graph. The points for Solly's income are: • (0 brochures, R0 income) • (100 brochures, R2000 income) • (200 brochures, R4000 income) Plot these points and draw a line through them on the same axes as the expenses graph. Step 5: Answer question 1.2.5. Solly's monthly expenses are equal to his monthly income when: Expenses = Income Using the formulas from Step 2 and Step 3 (where income is 20x): 10x + 1000 = 20x Subtract 10x from both sides: 1000 = 20x - 10x 1000 = 10x Divide by 10: x = (1000)/(10) x = 100 Solly's monthly expenses are equal to his monthly income when 100 brochures are printed. 100 brochures Step 6: Answer question 1.2.6. Calculate the profit for 160 brochures using the formula: Profit = Income - Expenses. First, calculate the Income for 160 brochures: Income = 20 × 160 Income = 3200 rand Next, calculate the Expenses for 160 brochures: Expenses = (10 × 160) + 1000 Expenses = 1600 + 1000 Expenses = 2600 rand Finally, calculate the Profit: Profit = Income - Expenses Profit = 3200 - 2600 Profit = 600 rand R600 What's next?