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The pizza was divided into 8 equal slices. Three friends each ate 2 slices. What is the ratio of slices eaten by the friends to the total number of slices? A map has a scale of 1 cm : 500 m. If a park

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

12 steps

7.

  1. Determine the total number of slices.

    The pizza was divided into 8 equal slices.
    Total slices =8= 8.

  2. Determine the number of slices the 3 friends had.

    Each of the 3 friends had 2 slices.
    Slices had by 3 friends =3×2=6= 3 \times 2 = 6.

  3. Form the ratio.

    The ratio of the number of slices the 3 friends had to the total number of slices is:

    Ratio=Slices had by 3 friendsTotal slices=68\text{Ratio} = \frac{\text{Slices had by 3 friends}}{\text{Total slices}} = \frac{6}{8}
  4. Simplify the ratio.

    Divide both the numerator and the denominator by their greatest common divisor, which is 2.

    6÷28÷2=34\frac{6 \div 2}{8 \div 2} = \frac{3}{4}

    The ratio is 3:43:4.

    The correct option is C. C. 3:4\boxed{\text{C. } 3:4}

    8.

  5. Understand the map scale.

    The scale is 1 cm on the map represents 500 m in actual distance.

    1 cm (map)=500 m (actual)1 \text{ cm (map)} = 500 \text{ m (actual)}
  6. Calculate the actual distance for 6 cm on the map.

    Map distance =6 cm= 6 \text{ cm}.
    Actual distance =6 cm×500 m1 cm=3000 m= 6 \text{ cm} \times \frac{500 \text{ m}}{1 \text{ cm}} = 3000 \text{ m}.

  7. Convert the actual distance to kilometers.

    Since 1 km=1000 m1 \text{ km} = 1000 \text{ m}, divide the distance in meters by 1000.

    Actual distance in km=3000 m1000 m/km=3 km\text{Actual distance in km} = \frac{3000 \text{ m}}{1000 \text{ m/km}} = 3 \text{ km}

    The correct option is C. C. 3km\boxed{\text{C. } 3\text{km}}

    9.

  8. Identify the departure and arrival times.

    Departure time =2:30 PM= 2:30 \text{ PM}.
    Arrival time =5:45 PM= 5:45 \text{ PM}.

  9. Calculate the duration in hours and minutes.

    From 2:30 PM to 5:45 PM:

    • From 2:30 PM to 3:00 PM is 30 minutes.
    • From 3:00 PM to 5:00 PM is 2 hours.
    • From 5:00 PM to 5:45 PM is 45 minutes. Total duration =2 hours+30 minutes+45 minutes=2 hours and 75 minutes= 2 \text{ hours} + 30 \text{ minutes} + 45 \text{ minutes} = 2 \text{ hours and } 75 \text{ minutes}. Since 75 minutes is 1 hour and 15 minutes, the total duration is 2 hours+1 hour and 15 minutes=3 hours and 15 minutes2 \text{ hours} + 1 \text{ hour and } 15 \text{ minutes} = 3 \text{ hours and } 15 \text{ minutes}.
  10. Convert the total duration to minutes.

    3 hours×60 minutes/hour+15 minutes3 \text{ hours} \times 60 \text{ minutes/hour} + 15 \text{ minutes} =180 minutes+15 minutes= 180 \text{ minutes} + 15 \text{ minutes} =195 minutes= 195 \text{ minutes}

    The correct option is D. D. 195\boxed{\text{D. } 195}

    10.

  11. Identify the departure and arrival times.

    Departure time =10:00 AM= 10:00 \text{ AM}.
    Arrival time =6:45 PM= 6:45 \text{ PM}.

  12. Calculate the duration in hours and minutes.

    • From 10:00 AM to 12:00 PM (noon) is 2 hours.
    • From 12:00 PM to 6:00 PM is 6 hours.
    • From 6:00 PM to 6:45 PM is 45 minutes. Total duration =2 hours+6 hours+45 minutes=8 hours and 45 minutes= 2 \text{ hours} + 6 \text{ hours} + 45 \text{ minutes} = 8 \text{ hours and } 45 \text{ minutes}.

    The correct option is A. A. 8 hours and 45 minutes\boxed{\text{A. } 8 \text{ hours and } 45 \text{ minutes}}

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