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A theater has three categories of tickets: Adult, Student, and Child. On Thursday, the number of attendees were: Adults (53, 57, 40), Students (15, 32, 10), and Children (9, 15, 9). Ticket prices for

Mathematics

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Answer

355.60 ZAR\text{355.60 ZAR}

Step-by-step solution

6 steps

  1. Calculate the total number of attendees for each category on Thursday.

    • Total Adults = 53+57+40=15053 + 57 + 40 = 150
    • Total Students = 15+32+10=5715 + 32 + 10 = 57
    • Total Children = 9+15+9=339 + 15 + 9 = 33

  2. Calculate the total revenue for Thursday, excluding VAT.

    The ticket prices for Thursday are: Adult = 28.60AUD,Student=28.60 AUD, Student = 26.40 AUD, Children = $17.60 AUD.

    Adult Revenue=150×28.60=4290.00 AUD\text{Adult Revenue} = 150 \times 28.60 = 4290.00 \text{ AUD} Student Revenue=57×26.40=1504.80 AUD\text{Student Revenue} = 57 \times 26.40 = 1504.80 \text{ AUD} Children Revenue=33×17.60=580.80 AUD\text{Children Revenue} = 33 \times 17.60 = 580.80 \text{ AUD} Total Revenue=4290.00+1504.80+580.80=6375.60 AUD\text{Total Revenue} = 4290.00 + 1504.80 + 580.80 = 6375.60 \text{ AUD}

  3. Verify the claim.

    The calculated total revenue for Thursday, excluding VAT, is 6375.60AUD.Theclaimstatesanamountof6375.60 AUD. The claim states an amount of 5796 AUD.
    Since 6375.60≠57966375.60 \neq 5796, the claim is incorrect.
    The claim that an amount of exactly $5796, excluding Australian VAT, was collected on that day is ❌ Incorrect.

  4. Calculate the cost of a Friday show ticket in South African Rand (ZAR).

    Assuming Nomzamo bought an adult ticket for a Friday show, the price is the same as Monday/Saturday.

    • Adult ticket price for Friday = $34.70 AUD

  5. Convert the ticket price from AUD to USD.

    Given 1 AUD = 0.71 USD.

    Price in USD=34.70 AUD×0.71USDAUD=24.637 USD\text{Price in USD} = 34.70 \text{ AUD} \times 0.71 \frac{\text{USD}}{\text{AUD}} = 24.637 \text{ USD}

  6. Convert the ticket price from USD to ZAR.

    Given 1 USD = 14.43 ZAR.

    Price in ZAR=24.637 USD×14.43ZARUSD=355.59951 ZAR\text{Price in ZAR} = 24.637 \text{ USD} \times 14.43 \frac{\text{ZAR}}{\text{USD}} = 355.59951 \text{ ZAR}

    Rounding to two decimal places:

    Price in ZAR=355.60 ZAR\text{Price in ZAR} = \boxed{\text{355.60 ZAR}}
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