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Math Help - Algebra Problem and Question

  1. #1
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    Question Algebra Problem and Question

    The sum of two numbers is 23. Seven times the first number less five times the second number is equal to 5. What are the two numbers?

    Now, i have worked this out and the numbers i get equal 23 but are not the numbers given as the answer in the book. Take a look:

    x + y = 23
    7x - 5y = 5
    7(23 - y) - 5y = 5
    161 - 7y - 5y = 5
    161 - 2y = 5
    2y = 156
    y = 78

    Put the numbers into the equation: -55 + 78 = 23

    So the answer i get appears to be correct because it works. But like i said, the answer in the back of the book is 10 + 13 = 23

    So where did i go wrong? And if algebra lead me to my answer (-55 + 78 = 23) which makes the equation true, why can't my answer be the right answer?
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  2. #2
    Junior Member Hardwork's Avatar
    Joined
    Sep 2010
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    x+y = 23, so y = 23-x

    7x-5y = 5, but y = 23-x from above, so

    7x-5(23-x) = 5

    7x-115+5x = 5

    7x+5x = 5+115

    12x = 120

    x = 10.

    x+y = 23

    10+y = 23

    so y = 23-10 = 13.
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  3. #3
    Junior Member Hardwork's Avatar
    Joined
    Sep 2010
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    Quote Originally Posted by Kick View Post
    161 - 7y - 5y = 5
    161 - 2y = 5
    Look again at this step.
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