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Solve for Δ in the equation 14 × Δ - 21 = 77. Also, calculate the total pay for a farm worker in 6 weeks if they earn R150 per day for 5 days each week.

Mathematics

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d) 14×Δ−21=7714 \times \Delta - 21 = 77

  1. Isolate the term with Δ\Delta.

    14×Δ=77+2114 \times \Delta = 77 + 21 14×Δ=9814 \times \Delta = 98
  2. Solve for Δ\Delta.

    Δ=9814\Delta = \frac{98}{14} Δ=7\Delta = 7

    Filling the table for problem d):

    problem solution (Δ\Delta)testconclusion
    714×7−21=98−21=7714 \times 7 - 21 = 98 - 21 = 7777=7777 = 77, correct

    The solution is Δ=7\boxed{\Delta = 7}.

    Support activity
    Problem: A farm worker get paid R150 + 5 days every week. How much in 6 weeks?

    Your final answer of R4500 is ✅ Correct.

    However, the number sentence you wrote, "R150 + 5 * 6", is incorrect for reaching R4500.
    The phrase "R150 + 5 days every week" is interpreted as the worker being paid R150 per day for 5 days each week.

  3. Determine the correct number sentence.

    Weekly pay is R150 per day for 5 days: 150×5150 \times 5.
    Total pay for 6 weeks: (150×5)×6(150 \times 5) \times 6.
    Correct number sentence: (150×5)×6=Total Pay(150 \times 5) \times 6 = \text{Total Pay}

  4. Calculate the total pay.

    First, calculate the weekly earnings:

    150×5=750150 \times 5 = 750

    Next, calculate the total earnings over 6 weeks:

    750×6=4500750 \times 6 = 4500

    The total amount the farm worker gets paid in 6 weeks is R4500\boxed{\text{R}4500}.

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