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Math Help - [Enigma] Small problems

  1. #16
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    Quote Originally Posted by Moo View Post
    What about 1 as a factor ?

    Since the girl can't know what the numbers are, *major hint* you have to find the triplets whose product is equal and whose sum is equal
    i still don't get this..
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  2. #17
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    Hello, Moo!

    3) Simple geometry
    The Swedish flag has a yellow cross of constant width in a blue background.
    The yellow area represents one-third of the flag's area.
    If the flag is 1m long and 66cm wide, what is the width of the yellow stripes ?

    The stripes comprising the cross can be "moved" to the edges of the flag.
    Let x = width of the stripe (cm).
    Code:
                  100
          * - - - - - - - - *
          |                 | x
          |   * - - - - - - * 
       66 |   |             |
          |   |             | 66-x
          |   |             |
          * - * - - - - - - *
            x      100-x

    The blue region's area is: . \frac{2}{3} \times (66\cdot100) \:=\;4400 cm²

    It is also: . (100-x)(66-x) cm²


    Hence, we have: . (100-x)(66-x) \:=\:4400 \quad\Rightarrow\quad x^2 - 166x + 2200 \:=\:0

    The Quadratic Formula gives us: . x \;=\;83 \pm3\sqrt{521}


    The smaller root is the answer: . x \;=\;83 - 3\sqrt{521} \;\approx\;14.52 cm.

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  3. #18
    A riddle wrapped in an enigma
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    Quote Originally Posted by Soroban View Post
    Hello, Moo!


    The stripes comprising the cross can be "moved" to the edges of the flag.
    Let x = width of the stripe (cm).
    Code:
                  100
          * - - - - - - - - *
          |                 | x
          |   * - - - - - - * 
       66 |   |             |
          |   |             | 66-x
          |   |             |
          * - * - - - - - - *
            x      100-x

    The blue region's area is: . \frac{2}{3} \times (66\cdot100) \:=\;4400 cm²

    It is also: . (100-x)(66-x) cm²


    Hence, we have: . (100-x)(66-x) \:=\:4400 \quad\Rightarrow\quad x^2 - 166x + 2200 \:=\:0

    The Quadratic Formula gives us: . x \;=\;83 \pm3\sqrt{521}


    The smaller root is the answer: . x \;=\;83 - 3\sqrt{521} \;\approx\;14.52 cm.

    See Post 10 for a different approach which yields the same result.
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