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Math Help - Least Number of Buses

  1. #1
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    Least Number of Buses

    For a class trip to the NY Aquarium, 461 students and 20 teachers will be taking buses in place of the subway. Each bus can seat a maximum of 52 persons. What is the least number of buses needed for this trip?

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    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by sharkman View Post
    For a class trip to the NY Aquarium, 461 students and 20 teachers will be taking buses in place of the subway. Each bus can seat a maximum of 52 persons. What is the least number of buses needed for this trip?
    To see how many number of busses you need, evaluate \frac{461+20}{52}. If you get a number with a decimal, round up to the nearest integer, and that will be your answer.
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    Now...

    Quote Originally Posted by Chris L T521 View Post
    To see how many number of busses you need, evaluate \frac{461+20}{52}. If you get a number with a decimal, round up to the nearest integer, and that will be your answer.
    The answer in the book is 10 buses. When I divide
    461 + 20 by 52, I get 9.25, which after being rounded to the nearest unit is 9. So, is the answer 9 buses or 10 buses?

    Thanks
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    You know the answer to this even though it is not readily obvious. Think of it this way:

    If I have 95 people going on a trip, and the buses I am using seat 9 people total, if I rent 10 buses, I will only be able to SEAT 90 people as each bus ONLY seats 10 people:

    9(people)*10(buses)=90 people on the bus.

    What happens to those other 5 people? They have to be seated in something. So the LEAST amount of buses I would need, would be 10 buses, to seat the remaining 5 people.

    This is a problem where we are dealing with WHOLE numbers. The reason you round up or down, is because you can not rent a PORTION of a quantity that is counted in whole numbers (1 bus, 2 buses, 3 buses, etc. - not 1.5 buses, 2.5 buses. . .). If you round 9.25 DOWN (from your original problem), you have people left out in the rain. If you round 9.25 UP you will get 10 buses, and be able to seat everyone.

    Soon you will learn a pair of functions called the Greatest/Least Integer Function, and these functions are based on the idea that you round up or down in relation to an integer to find the greatest or least integer related to your number. Cell phone companies operate on this level in regards to your minutes. You wont (rarely) be charged for 100.7 or 100.3 minutes: you'll be charged 101 minutes.
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    ok...

    Quote Originally Posted by ANDS! View Post
    You know the answer to this even though it is not readily obvious. Think of it this way:

    If I have 95 people going on a trip, and the buses I am using seat 9 people total, if I rent 10 buses, I will only be able to SEAT 90 people as each bus ONLY seats 10 people:

    9(people)*10(buses)=90 people on the bus.

    What happens to those other 5 people? They have to be seated in something. So the LEAST amount of buses I would need, would be 10 buses, to seat the remaining 5 people.

    This is a problem where we are dealing with WHOLE numbers. The reason you round up or down, is because you can not rent a PORTION of a quantity that is counted in whole numbers (1 bus, 2 buses, 3 buses, etc. - not 1.5 buses, 2.5 buses. . .). If you round 9.25 DOWN (from your original problem), you have people left out in the rain. If you round 9.25 UP you will get 10 buses, and be able to seat everyone.

    Soon you will learn a pair of functions called the Greatest/Least Integer Function, and these functions are based on the idea that you round up or down in relation to an integer to find the greatest or least integer related to your number. Cell phone companies operate on this level in regards to your minutes. You wont (rarely) be charged for 100.7 or 100.3 minutes: you'll be charged 101 minutes.
    Thank you for explaining more in detail.
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    ok...

    Quote Originally Posted by ANDS! View Post
    You know the answer to this even though it is not readily obvious. Think of it this way:

    If I have 95 people going on a trip, and the buses I am using seat 9 people total, if I rent 10 buses, I will only be able to SEAT 90 people as each bus ONLY seats 10 people:

    9(people)*10(buses)=90 people on the bus.

    What happens to those other 5 people? They have to be seated in something. So the LEAST amount of buses I would need, would be 10 buses, to seat the remaining 5 people.

    This is a problem where we are dealing with WHOLE numbers. The reason you round up or down, is because you can not rent a PORTION of a quantity that is counted in whole numbers (1 bus, 2 buses, 3 buses, etc. - not 1.5 buses, 2.5 buses. . .). If you round 9.25 DOWN (from your original problem), you have people left out in the rain. If you round 9.25 UP you will get 10 buses, and be able to seat everyone.

    Soon you will learn a pair of functions called the Greatest/Least Integer Function, and these functions are based on the idea that you round up or down in relation to an integer to find the greatest or least integer related to your number. Cell phone companies operate on this level in regards to your minutes. You wont (rarely) be charged for 100.7 or 100.3 minutes: you'll be charged 101 minutes.
    Thanks for the detailed reply.
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