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The table below lists various tools, materials, and components needed to construct a basic circuit project. Prices already include 15% VAT. Some values are missing and must be calculated.

Mathematics

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Step-by-step solution

5 steps

Here are the calculations to complete the table and determine the total cost and VAT charged.

  1. Calculate missing Unit Prices and Quantities.

    • Item 1: Battery holder
      • Unit Price = Amount / Quantity
      • Unit Price=R336,004=R84,00\text{Unit Price} = \frac{\text{R}336,00}{4} = \text{R}84,00
    • Item 2: Glue Sticks 100g
      • Quantity = Amount / Unit Price
      • Quantity=R295,00R59,00=5\text{Quantity} = \frac{\text{R}295,00}{\text{R}59,00} = 5
    • Item 3: LED (pack of 100)
      • Unit Price = Amount / Quantity
      • Unit Price=R352,001=R352,00\text{Unit Price} = \frac{\text{R}352,00}{1} = \text{R}352,00
  2. Calculate missing Amounts.

    • Item 5: Battery Pack of 4 (Duracell)
      • Amount = Quantity ×\times Unit Price
      • Amount=2×R96,00=R192,00\text{Amount} = 2 \times \text{R}96,00 = \text{R}192,00
    • Item 8: Resistors
      • Amount = Quantity ×\times Unit Price
      • Amount=2×R12,35=R24,70\text{Amount} = 2 \times \text{R}12,35 = \text{R}24,70
    • Item 9: Acrylic Poster Paint (6 colours included)
      • Amount = Quantity ×\times Unit Price
      • Amount=2×R225,00=R450,00\text{Amount} = 2 \times \text{R}225,00 = \text{R}450,00
  3. Complete the table with all calculated values.

    ITEM NoDescription of ItemQUANTITYUnit Price (including VAT)Amount
    1Battery holder4R84,00R336,00
    2Glue Sticks 100g5R59,00R295,00
    3LED (pack of 100)1 packR352,00R352,00
    4Glue Gun1R169,00R169,00
    5Battery Pack of 4 (Duracell)2 packsR96,00R192,00
    6Buzzer1R26,95R26,95
    7Connecting wire per meter1R5,00R5,00
    8Resistors2R12,35R24,70
    9Acrylic Poster Paint (6 colours)2 packsR225,00R450,00
    10Cardboard (2m x 2m)1R25,88R25,88
  4. Calculate the Total Cost.

    The Total Cost is the sum of all amounts in the "Amount" column.

    Total Cost=R336,00+R295,00+R352,00+R169,00+R192,00+R26,95+R5,00+R24,70+R450,00+R25,88\text{Total Cost} = \text{R}336,00 + \text{R}295,00 + \text{R}352,00 + \text{R}169,00 + \text{R}192,00 + \text{R}26,95 + \text{R}5,00 + \text{R}24,70 + \text{R}450,00 + \text{R}25,88 Total Cost=R1876,53\text{Total Cost} = \text{R}1876,53

    The total cost is R1876,53\boxed{\text{R}1876,53}.

  5. Calculate the VAT Charged.

    Since the prices already include 15% VAT, the total cost (R1876,53) represents 115% of the price excluding VAT.
    To find the VAT amount, we can use the formula:

    VAT Charged=Total Cost−Total Cost1+VAT Rate\text{VAT Charged} = \text{Total Cost} - \frac{\text{Total Cost}}{1 + \text{VAT Rate}} VAT Charged=R1876,53−R1876,531+0.15\text{VAT Charged} = \text{R}1876,53 - \frac{\text{R}1876,53}{1 + 0.15} VAT Charged=R1876,53−R1876,531.15\text{VAT Charged} = \text{R}1876,53 - \frac{\text{R}1876,53}{1.15} VAT Charged=R1876,53−R1631,77\text{VAT Charged} = \text{R}1876,53 - \text{R}1631,77 VAT Charged=R244,76\text{VAT Charged} = \text{R}244,76

    The VAT charged is R244,76\boxed{\text{R}244,76}.

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