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Miss Nolan wants to bake 80 brownies. Each batch of brownies has 16 brownies. The preparation for each batch takes 15 minutes and baking takes 35 minutes. If she wants to finish baking at 16:45, what

Mathematics

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1.3.1

  1. Identify the total number of brownies Miss Nolan wants to bake.

    Miss Nolan wants to bake 80 brownies.

  2. Identify the number of brownies per batch.

    From the "NOTE" section, 1 batch = 16 brownies.

  3. Calculate the number of batches needed.

    Number of batches=Total browniesBrownies per batch\text{Number of batches} = \frac{\text{Total brownies}}{\text{Brownies per batch}} Number of batches=8016\text{Number of batches} = \frac{80}{16} Number of batches=5\text{Number of batches} = 5

    Miss Nolan needs to bake 5 batches\boxed{\text{}5 \text{ batches}}.

    1.3.2

  4. Identify the desired finish time for baking.

    The baking must be finished at $16:45$.

  5. Identify the preparation time and baking time for one batch.

    Preparation time = 15 minutes
    Baking time = 35 minutes

  6. Calculate the total time required for the first batch (preparation + baking).

    Total time for first batch=Preparation time+Baking time\text{Total time for first batch} = \text{Preparation time} + \text{Baking time} Total time for first batch=15 minutes+35 minutes\text{Total time for first batch} = 15 \text{ minutes} + 35 \text{ minutes} Total time for first batch=50 minutes\text{Total time for first batch} = 50 \text{ minutes}
  7. Calculate the start time for preparing the first batch.

    Start time=Finish time−Total time for first batch\text{Start time} = \text{Finish time} - \text{Total time for first batch} Start time=16:45−50 minutes\text{Start time} = 16:45 - 50 \text{ minutes}

    To subtract 50 minutes from 16:4516:45:
    16 hours 45 minutes−50 minutes16 \text{ hours } 45 \text{ minutes} - 50 \text{ minutes}
    Since 45<5045 < 50, borrow 1 hour (60 minutes) from 16 hours.
    15 hours (60+45) minutes−50 minutes15 \text{ hours } (60 + 45) \text{ minutes} - 50 \text{ minutes}
    15 hours 105 minutes−50 minutes15 \text{ hours } 105 \text{ minutes} - 50 \text{ minutes}
    15 hours 55 minutes15 \text{ hours } 55 \text{ minutes}
    The start time is 15:55\boxed{\text{}15:55} .

    1.3.3

  8. Identify the baking temperature in Fahrenheit.

    The baking temperature is 330∘F330^\circ \text{F}.

  9. Use the given formula to convert Fahrenheit to Celsius.

    The formula is ∘C=(∘F−32)÷1,8^\circ \text{C} = (^\circ \text{F} - 32) \div 1,8.
    Substitute ∘F=330^\circ \text{F} = 330:

    ∘C=(330−32)÷1,8^\circ \text{C} = (330 - 32) \div 1,8
  10. Perform the calculation.

    ∘C=298÷1,8^\circ \text{C} = 298 \div 1,8 ∘C≈165.555...^\circ \text{C} \approx 165.555...
  11. Round the answer to the nearest 10 degrees Celsius.

    165.555... is between 160 and 170. Since 165.555... is closer to 170 than to 160, we round up.

    ∘C≈170∘C^\circ \text{C} \approx 170^\circ \text{C}

    The baking temperature in Celsius, rounded to the nearest 10 degrees, is 170∘C\boxed{\text{}170^\circ \text{C}}.

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