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Calculate the missing value A the amount in her online shopping basket, Determine the selling price of one t-shirt, Write down a formula that can be used to calculate the total income received, and Calculate the missing value B.

Mathematics

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Step-by-step solution

4 steps
  1. Calculate the missing value A.

    Value A represents the total cost for Vinyl. This is calculated by multiplying the amount of Vinyl by its price per unit.

    A=Amount of Vinyl×Price per unit of VinylA = \text{Amount of Vinyl} \times \text{Price per unit of Vinyl} A=5×R160.40A = 5 \times \text{R}160.40 A=R802.00A = \text{R}802.00

    We can also verify this using the total payable:

    Total Payable=Total for White T-shirts+A\text{Total Payable} = \text{Total for White T-shirts} + A R14 000=R13 198.00+A\text{R}14\,000 = \text{R}13\,198.00 + A A=R14 000−R13 198.00A = \text{R}14\,000 - \text{R}13\,198.00 A=R802.00A = \text{R}802.00

    The missing value A is R802.00\boxed{\text{R}802.00}.

  2. Determine the selling price of one t-shirt.

    From TABLE 1, we can use the 'Revenue (Rand)' for a given 'NUMBER OF TSHIRTS'. For example, for 25 t-shirts, the revenue is R2250.

    Selling price per t-shirt=Total RevenueNumber of T-shirts\text{Selling price per t-shirt} = \frac{\text{Total Revenue}}{\text{Number of T-shirts}} Selling price per t-shirt=R225025\text{Selling price per t-shirt} = \frac{\text{R}2250}{25} Selling price per t-shirt=R90\text{Selling price per t-shirt} = \text{R}90

    Let's check with another data point, e.g., 50 t-shirts and R4500 revenue:

    Selling price per t-shirt=R450050=R90\text{Selling price per t-shirt} = \frac{\text{R}4500}{50} = \text{R}90

    The selling price of one t-shirt is R90\boxed{\text{R}90}.

  3. Write down a formula that can be used to calculate the total income received.

    Total income is the total revenue. Based on the selling price calculated in Step 2, the formula for total income is the selling price per t-shirt multiplied by the number of t-shirts.

    Total Income=Selling Price per t-shirt×Number of T-shirts\text{Total Income} = \text{Selling Price per t-shirt} \times \text{Number of T-shirts}

    Using the selling price of R90:

    Total Income=R90×Number of T-shirts\boxed{\text{Total Income} = \text{R}90 \times \text{Number of T-shirts}}
  4. Calculate the missing value B.

    The problem states that the total expenses can be calculated by the formula: Expenses=R70×number of t-shirts\text{Expenses} = \text{R}70 \times \text{number of t-shirts}.
    From TABLE 1, the missing value B corresponds to 50 t-shirts.

    B=R70×Number of T-shirts\text{B} = \text{R}70 \times \text{Number of T-shirts} B=R70×50\text{B} = \text{R}70 \times 50 B=R3500\text{B} = \text{R}3500

    The missing value B is R3500\boxed{\text{R}3500}.

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