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Math Help - Word Algebra Problem

  1. #1
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    Word Algebra Problem

    Hi!

    J'onn J'onnz worked 7 more problems than Clark Kent. Together they worked 55 problems. How many did each boy work?

    I got 31 for J'onn and 24 for Clark:

    J'onn = J
    Clark = C

    J = 7 + C
    7 + C = 55
    C = 48

    48/2 = 24 ==> Clark
    24 + 7 = 31 ==> J'onn

    Another way is: 55 + 7 = 62
    62/2 = 31
    31 - 7 = 24

    I think my methods are flawed and that's the reason for my seeking help.
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  2. #2
    Super Member Quacky's Avatar
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    Re: Word Algebra Problem

    I don't understand the method. It may be correct and valid, I just don't understand it.

    I agree with J=7+C

    Together they worked 55 problems.
    So:

    J+C=55

    We have two equations:
    J=7+C
    J+C=55

    I'd substitute the first into the second, to get:
    (7+C)+C=55
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  3. #3
    Junior Member mathbyte's Avatar
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    Re: Word Algebra Problem

    One more point to what Quacky said:
    You were asked the question "how many problems did each boy work?"
    By that question being asked, you know there are two unknowns to find.
    For x unknowns, you need x equations to solve for them.
    Thus, for two unknowns, you need to establish two equations based on the given information to find them.
    Once you have the same number of equations as unknowns, you can then start to solve the problem. Quacky suggested substituting one equation into the other one and that's definitely your best bet.
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  4. #4
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    Re: Word Algebra Problem

    Quote Originally Posted by Hellbent View Post
    Hi!

    J'onn J'onnz worked 7 more problems than Clark Kent. Together they worked 55 problems. How many did each boy work?

    I got 31 for J'onn and 24 for Clark:

    J'onn = J
    Clark = C

    J = 7 + C
    7 + C = 55
    No, J+ C= 55 so (7+ C)+ C= 7+ 2C= 55

    C = 48
    No, 2C= 48 so C= 48/2= 24

    48/2 = 24 ==> Clark
    Okay, now you have the correct value- but you had said before "Clark = C" by which I assume you meant that C was the number of problems Clark worked. Having said that, it makes no sense to say "7+ C= 55" or to divide C by 2 to get the number of problems Clark worked.

    24 + 7 = 31 ==> J'onn

    Another way is: 55 + 7 = 62
    Why? What part of the statement of this problem leads you to add 7 to 62?
    62/2 = 31

    31 - 7 = 24

    I think my methods are flawed and that's the reason for my seeking help.
    You do come to the correct answer but what logic led you to it?

    It is true that if J= 7+ C so C= J- 7. Then J+ C= J+ J- 7= 2J- 7= 55. Now you have that 2J= 55+ 7= 62 and then J= 31. If that was your reasoning, great- but say so!
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