Mr. Smith offers students two paying options for training. The first option costs R 1 025 per hour plus an additional of R4 800. The second option cost R1 345 per hour with no annual amount.

Question

Asked on July 18, 2026Mathematics

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.

Accepted Answer · 2026-07-18T09:22:56.249Z

Here are the solutions to your questions: 3.1.1 Step 1: Determine the formulas for Option 1 and Option 2. Option 1: Cost (C_1) = R 1 025 per hour + R 4 800. So, C_1 = 1025H + 4800. Option 2: Cost (C_2) = R 1 345 per hour. So, C_2 = 1345H. Step 2: Calculate the missing values using the formulas. For A (Option 1, H=0): A = 1025(0) + 4800 = 4800 For B (Option 1, H=20): B = 1025(20) + 4800 = 20500 + 4800 = 25300 For C (Option 2, H=10): C = 1345(10) = 13450 For D (Option 1, C_1 = 56050): 56050 = 1025D + 4800 56050 - 4800 = 1025D 51250 = 1025D D = (51250)/(1025) = 50 For E (Option 1, H=40): E = 1025(40) + 4800 = 41000 + 4800 = 45800 For F (Option 2, H=40): F = 1345(40) = 53800 The missing values are: A: R 4800 B: R 25300 C: R 13450 D: 50 hours E: R 45800 F: R 53800 3.1.2 The formula for Option 1 is: C_1 = 1025H + 4800 where C_1 is the cost and H is the number of hours. 3.1.3 The dependent variable is the Cost (R). Reason: The cost depends on the number of hours worked; as the number of hours changes, the total cost changes. 3.1.4 To draw the graphs: • Heading: Cost of Training Options vs. Number of Hours • X-axis: Label "Number of Hours (H)". Scale from 0 to 50, perhaps in increments of 5 or 10. • Y-axis: Label "Cost (R)". Scale from 0 to 70000, perhaps in increments of 5000 or 10000. • Plot points for Option 1: (0, 4800), (5, 9925), (10, 15050), (20, 25300), (30, 35550), (40, 45800), (50, 56050). Connect these points with a straight line and label it "Option 1". • Plot points for Option 2: (0, 0), (5, 6725), (10, 13450), (20, 26900), (30, 40350), (40, 53800), (50, 67250). Connect these points with a straight line and label it "Option 2". • Break-even point: Mark the intersection of the two lines. 3.1.5 Step 1: Set the costs of the two options equal to find the break-even point. C_1 = C_2 1025H + 4800 = 1345H Step 2: Solve for H. 4800 = 1345H - 1025H 4800 = 320H H = (4800)/(320) H = 15 hours Step 3: Substitute H=15 into either cost formula to find the rand value. Using Option 1: C_1 = 1025(15) + 4800 = 15375 + 4800 = 20175 Using Option 2: C_2 = 1345(15) = 20175 The break-even point is 15 hours and R 20175. What's next? Send 'em! 📸

Accepted Answer · 2026-07-18T09:22:56.249Z

Here are the solutions to your questions: 3.1.1 Step 1: Determine the formulas for Option 1 and Option 2. Option 1: Cost (C_1) = R 1 025 per hour + R 4 800. So, C_1 = 1025H + 4800. Option 2: Cost (C_2) = R 1 345 per hour. So, C_2 = 1345H. Step 2: Calculate the missing values using the formulas. For A (Option 1, H=0): A = 1025(0) + 4800 = 4800 For B (Option 1, H=20): B = 1025(20) + 4800 = 20500 + 4800 = 25300 For C (Option 2, H=10): C = 1345(10) = 13450 For D (Option 1, C_1 = 56050): 56050 = 1025D + 4800 56050 - 4800 = 1025D 51250 = 1025D D = (51250)/(1025) = 50 For E (Option 1, H=40): E = 1025(40) + 4800 = 41000 + 4800 = 45800 For F (Option 2, H=40): F = 1345(40) = 53800 The missing values are: A: R 4800 B: R 25300 C: R 13450 D: 50 hours E: R 45800 F: R 53800 3.1.2 The formula for Option 1 is: C_1 = 1025H + 4800 where C_1 is the cost and H is the number of hours. 3.1.3 The dependent variable is the Cost (R). Reason: The cost depends on the number of hours worked; as the number of hours changes, the total cost changes. 3.1.4 To draw the graphs: • Heading: Cost of Training Options vs. Number of Hours • X-axis: Label "Number of Hours (H)". Scale from 0 to 50, perhaps in increments of 5 or 10. • Y-axis: Label "Cost (R)". Scale from 0 to 70000, perhaps in increments of 5000 or 10000. • Plot points for Option 1: (0, 4800), (5, 9925), (10, 15050), (20, 25300), (30, 35550), (40, 45800), (50, 56050). Connect these points with a straight line and label it "Option 1". • Plot points for Option 2: (0, 0), (5, 6725), (10, 13450), (20, 26900), (30, 40350), (40, 53800), (50, 67250). Connect these points with a straight line and label it "Option 2". • Break-even point: Mark the intersection of the two lines. 3.1.5 Step 1: Set the costs of the two options equal to find the break-even point. C_1 = C_2 1025H + 4800 = 1345H Step 2: Solve for H. 4800 = 1345H - 1025H 4800 = 320H H = (4800)/(320) H = 15 hours Step 3: Substitute H=15 into either cost formula to find the rand value. Using Option 1: C_1 = 1025(15) + 4800 = 15375 + 4800 = 20175 Using Option 2: C_2 = 1345(15) = 20175 The break-even point is 15 hours and R 20175. What's next? Send 'em! 📸

Mr. Smith offers students two paying options for training. The first option costs R 1 025 per hour plus an additional of R4 800. The second option cost R1 345 per hour with no annual amount.

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Mr. Smith offers students two paying options for training. The first option costs R 1 025 per hour plus an additional of R4 800. The second option cost R1 345 per hour with no annual amount.

Need help with your own homework?

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