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Math Help - Word Problem

  1. #1
    Newbie
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    Nov 2009
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    5

    Word Problem

    Please help me solve this at the latest by tomorrow morning. Thanks


    I) Anticipating significant growth i n the air travel industry, you placed orders
    totaling $2100 million to purchase new aircraft that would seat a total of
    4500 passengers. Some of the aircraft were Boeing 747s that cost $200
    million each and seat 400 passengers and Boeing 777s that cost $160 million
    each and seat 300 passengers. Others are European Airbus A321s that cost
    $60 million and seat 200 passengers. At the time you were instructed to
    buy twice as many US manufactured aircraft as foreign aircraft.

    a) Given the selection of three aircraft, how many of each type of aircraft did
    you order?

    II) Due to recent economic conditions you have been told to alter the order
    for new equipment you made several years ago. The new aircraft had
    not been received and placed into service yet because of the long lead
    time to manufacture such complex and sophisticated equipment. The
    revised budget for new aircraft is now $1810 million for 800 fewer total
    passenger seats. At this point in production Boeing charges $40 million
    for each 747 aircraft canceled and $35 million for each 777 aircraft
    canceled. In a similar fashion Airbus charges $20 million for each A321
    aircraft canceled.

    b) Given that all other criteria remain the same, how many of each type of
    aircraft did you cancel?
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  2. #2
    MHF Contributor
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    Talking

    Start by naming things. Since you are asked for the numbers of each type of plane, pick variables to stand for these unknowns.

    x: number of 747s
    y: number of 777s
    z: number of A321s

    You are given a relationship between the types of planes, the cost of one of each, and the total spent. Use this relationship to create an equation.

    You are given a relationship between the types of planes, the seating in one of each, and the total seating ordered. Use this relationship to create an equation.

    You are given a relationship between the total number of 747s and 777s and the number of A321s. Use this relationship to create an equation.

    You now have three equations in three unknowns. Solve the system for the values of the variables.

    The second exercise works similarly. If you get stuck on either, please reply showing what you have tried and how far you have gotten. Thank you!
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  3. #3
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    word problem

    I tried to setup the two equations, but cannot get the third one:

    The first one I got is:

    200x+160y+60z=2100

    The second one is:

    400x+300y+200z=4500

    Can't get the third one but I tried:

    2x+2y+z=3

    Where did I go wrong?
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  4. #4
    MHF Contributor
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    Talking

    Where did the "3" come from? You're given that (total of American planes) is (twice)(number of European planes), with "is" being "equals", of course. Try using the given relationship instead of whatever you're trying with the "3".
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  5. #5
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    Nov 2009
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    Word problem...

    Thanks for the help in Part A. For part B I got the following equations:

    1) -40x-35y-20z=290
    2) 400x+300y+200z=3700
    3) x+y-2z=0

    I am getting the following for:

    x= 113
    y= -132
    z=-9.5

    but these numbers don't make any sense. I think I have done something wrong. Please help.
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