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Thread: Football club, how many showed up for pratic.

  1. #1
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    Smile Football club, how many showed up for pratic.

    The football club has pratic one day.
    1/4 did powerlifting
    2/5 did technical training.
    and the remaning 21 did cardio.

    How many showed up for pratic this day?
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  2. #2
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    Re: Football club, how many showed up for pratic.

    Let X be the total number that showed up.
    "1/4 did powerlifting" That's (1/4)X= X/4 people

    "2/5 did technical training." That's (2/5)X= 2X/5 people

    "and the remaining 21 did cardio" That's 21 people

    The total is X/4+ 2X/5+ 21= X.

    Solve that for X. I would start by subtracting X/4 and 2X/5 form both sides. However I think you will find that this is impossible. X does not turn out to be a whole number.
    Last edited by HallsofIvy; Apr 20th 2018 at 04:24 AM.
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by HallsofIvy View Post
    Let X be the total number that showed up.
    "1/4 did powerlifting" That's (1/4)X= X/4 people

    "2/5 did technical training." That's (2/5)X= 2X/5 people

    "and the remaining 21 did cardio" That's 21 people

    The total is X/4+ 2X/5+ 21= X.

    Solve that for X. I would start by subtracting X/4 and 2X/5 form both sides. However I think you will find that this is impossible. X does not turn out to be a whole number.

    X/4+ 2X/5+ 21= X.

    X x 20 /4 + 2X x 20 / 5 + 21 = X

    X x 5 + 2X x 4 + 21 = X

    5X + 8X + 21 = X

    13X + 21 = X

    13X - X = -21

    12X = -21

    12X / 12 = -21 / 12

    X = -1.75

    Am i on the right track and if soo, wher do i go from her?
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    Re: Football club, how many showed up for pratic.

    $n$ folks showed up

    $\dfrac{n}{4} + \dfrac{2n}{5} + 21 = n$

    $\dfrac{5n}{20}+\dfrac{8n}{20} + 21 = n$

    $\dfrac{13}{20}n + 21 = n$

    $21 = \dfrac{7}{20}n$

    $n = 60$
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by Greb View Post
    The football club has pratic one day.
    1/4 did powerlifting
    2/5 did technical training.
    and the remaning 21 did cardio.
    How many showed up for pratic this day?
    Lets find a common denominator: $\frac{1}{4}=\frac{5}{20}~\&~\frac{2}{5}=\frac{8}{ 20}$.
    Thus the remaining $21$ form $\frac{7}{20}$ of the whole. So $X=60$.
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by romsek View Post
    $n$ folks showed up

    $\dfrac{n}{4} + \dfrac{2n}{5} + 21 = n$

    $\dfrac{5n}{20}+\dfrac{8n}{20} + 21 = n$

    $\dfrac{13}{20}n + 21 = n$

    $21 = \dfrac{7}{20}n$

    $n = 60$


    $\dfrac{13}{20}n + 21 = n$

    $21 = \dfrac{7}{20}n$

    what happend her?
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by Greb View Post
    $\dfrac{13}{20}n + 21 = n$

    $21 = \dfrac{7}{20}n$

    what happend her?
    really?

    multiply both sides of the equation by $\dfrac{20}{7}$
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  8. #8
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by Greb View Post
    $\dfrac{13}{20}n + 21 = n$

    $21 = \dfrac{7}{20}n$

    what happend her?
    $n = 1\cdot n = \dfrac{20}{20}\cdot n$

    $\dfrac{13}{20}n + 21 = n$

    $\dfrac{13}{20}n + 21 = \dfrac{20}{20}n$

    $\dfrac{13}{20}n+21 - \dfrac{13}{20}n = \dfrac{20}{20}n - \dfrac{13}{20}n$ (what you do to one side, you must do to both)

    $\cancel{\dfrac{13}{20}n} + 21 - \cancel{\dfrac{13}{20}n} = \dfrac{20-13}{20} n = \dfrac{7}{20}n$

    $21 = \dfrac{7}{20}n$
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by romsek View Post

    $21 = \dfrac{7}{20}n$

    $n = 60$
    sorry, i meant to ask for this part. what happend her?
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  10. #10
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    Re: Football club, how many showed up for pratic.

    Quote Originally Posted by Greb View Post
    sorry, i meant to ask for this part. what happend her?
    Then, as romsek said, multiply both sides by $\dfrac{20}{7}$.
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