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Math Help - Story Problems, please help! :)

  1. #1
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    Story Problems, please help! :)

    1. Each of eighteen students was given a different integer from 1 through 18, inclusive. When asked to select a dance partner, the sum of the numbers for each of the nine couples was a perfect square. Who was dancing with whom?

    2. In a 10-foot-wide alley, two ladders lean against opposite walls. One ladder reaches 30 feet up the wall, the other ladder reaches 20 feet high. The bases of the ladders rest against opposite walls. How high above the ground will the ladders cross?

    3. A 100-pound watermellon is 95% water. It is dehydrated until it is 90% water. What is its weight after dehydration?

    4. The flag of the United States has 13 stripes, alternating red and white, with a blue canton containing 50 stars. An American flag that is 78" by 136" with a canton that is 42" by 51" is wat percent red?


    Any help would be much appreciated! Thanks!
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  2. #2
    Senior Member Danneedshelp's Avatar
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    Given the relation R=\{aRb | a+b=perfect square\leq{25}\}, the couples are \{(1,15),(2,14),(3,13),(4,12),(5,11),(6,10),(7,18)  , (8,17),(9,16)\}
    Last edited by Danneedshelp; July 25th 2009 at 10:28 PM.
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  3. #3
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    Quote Originally Posted by epetrik View Post
    ...

    2. In a 10-foot-wide alley, two ladders lean against opposite walls. One ladder reaches 30 feet up the wall, the other ladder reaches 20 feet high. The bases of the ladders rest against opposite walls. How high above the ground will the ladders cross?

    ...
    1. Draw a sketch.

    2. You get 2 proportions.
    Left right triangle:

    \dfrac hx=\dfrac{20}{10}~\implies~x=\dfrac12 h

    Right right triangle:

    \dfrac h{10-x}=\dfrac{30}{10}

    3. Substitute x by the term from the first equation and solve for h.

    \dfrac h{10-\dfrac12 h}=\dfrac{30}{10}

    Spoiler:
    For your confirmation only: h = 12
    Attached Thumbnails Attached Thumbnails Story Problems, please help! :)-leiter_imschacht.png  
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  4. #4
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    Quote Originally Posted by epetrik View Post
    ...

    3. A 100-pound watermellon is 95% water. It is dehydrated until it is 90% water. What is its weight after dehydration?

    ...
    1. The melon contains 5% dry material = 5 pounds.

    2. Let x denote the amount of water which has been taken from the melon. Then you know:

    \dfrac{\overbrace{100-5-x}^{water\ left}}{\underbrace{100-x}_{actual\ weight}}=0.9

    3. Solve for x.

    Spoiler:
    For your confirmation only:
    Spoiler:
    x = 50, that means the actual weight is 50 pounds too


    There is a shortcut:

    1. The melon contains 5 pounds of dry material.
    2. These 5 pounds are 10% of the dried melon.
    3. Thus the melon must weigh 50 pounds.
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