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Thread: Correction help with this

  1. #1
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    Correction help with this

    The sum of two numbers is 78. If the smaller number is 12 less than one- fifth of the larger number, find the two numbers.

    Attempt 1

    a + a + 12 - a/5 = 78

    5a + 5a + (5)12 - (5) a/5 = 78 * 5

    5a + 5a + 60 - a = 390

    9a = 390 - 60

    9a = 330

    a = 3.66

    Attempt 2

    A + 12 (1/5)a = 78 :

    I think the second attempt is completely wrong
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  2. #2
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    Re: Correction help with this

    $a+b=78$

    let $a < b$

    $a=\dfrac 1 5 b - 12$

    $b + \dfrac 1 5 b - 12 = 78$

    $\dfrac{6}{5}b = 90$

    $b = 90 \cdot \dfrac{5}{6} = 75$

    $a = \dfrac{75}{5}-12 = 3$

    $(a,b) = (3,75)$
    Thanks from diehardmath4
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  3. #3
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    Re: Correction help with this

    So the equation is substitution elimination ?
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  4. #4
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    Re: Correction help with this

    Quote Originally Posted by diehardmath4 View Post
    So the equation is substitution elimination ?
    I'm sorry I don't know what that means.

    I just call it algebra.
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  5. #5
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    Re: Correction help with this

    diehardmath4, where did you get "a + a + 12 - a/5 = 78"? What was your reasoning? I can guess that the "12- a/5" is from "twelve less than 1/5 the number" but "12 less than" something is that something minus 12, not 12 minus something. And then, I guess, "a" is the first number. But why do you have "a+ a"?
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