Maths homework - inequality

Discussion in 'General Discussion' started by Tahir2, Jan 14, 2018.

  1. Tahir2

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    Hey there

    Trying to help my daughter with some math homework.

    Pam is 7 years younger than Amanda. Amanda is u years old.
    a) write an expression for Pam's age.
    b) Pam is 16 years old or older. Show this as an inequality.
    c) Solve this to show an inequality for Amanda's age.

    What I have is:

    a) 7 - u > p
    b) 16p > 7 - u
    c)) 23 >

    ???
    And another one...

    Tim is half Jill's age, Jill is b years.
    a) write an expression for Jill's age.
    b) Tim is 14 years old or younger, show this as an inequality.
    c) Show an inequality for Jill's age.

    Never done these before, am I even on the right track....
     
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  2. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    Here's how I'm initially parsing things. The first expression A is an exact statement, not an inequality. For statement B you use substitution for pam's age (p) in relations to Amanda's (u -7).

    a) u - 7 = p
    b) p >= 16
    u - 7 >= 16

    c) u - 7 >= 16
    u >= 16 + 7
    u >= 23
     
  3. Tahir2

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    It is an inequality as Pam is 16 years old or older. Or so I thought.
     
  4. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    For the second part my logic after only 4 hours of sleep { big ole disclaimer, so look for obvious mistakes, but here's how I processed it with logic } ...

    [ we use t for Tim's age and j for Jill's age ]
    t = 1/2 j
    [ multiply both sides by 2 to normalize for j ]
    2 * t = j
    [ now we use 'b' for jills age ]
    2 * t = b
    [ written for b as base statement on left side]
    b = 2 * t

    a) b = 2 * t
    b) t <= 14
    c) b <= 2 * t
    b <= 2 * 14
    b <= 28
     
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  5. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    Yes, but that doesn't come into play until step C.
    I took it one statement at a time and worked with that.

    "Pam is 7 years younger than Amanda."
    p = Amanda - 7

    Next we plug in the second statement: "Amanda is u years old."
    p = u - 7.


    Of course, many people can apply things in different orders, and this is just how I processed it.

    I added more step descriptions in my second response for the next part.

    Hope this helps, as I know it's really rough having to help children with homework as they likely change the way they want them to work or show their work. Despite nearly having a BS in Applied Mathematics (almost double major to go with my BS in Comp.Sci) I can't even help my 7 year old niece on her homework because of "Common Core" methods in the US.

    It's rough, but hang in there and talk with them to try to reason it out. I find it far better to have them understand the steps of problem solving than it is to force a specific method on them.
     
  6. Silent_Buddha

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    There are many ways to represent things.

    Pam is 7 years younger than Amanda.
    1. Pam = Amanda - 7
    2. Pam + 7 = Amanda
    Write an expression for Pam's age. Since 2 above is a function of Amanda, you'd use 1 above and substitute variables.
    • p = u - 7
    Pam is 16 years or older, show this as an inequality.
    • p >= 16
      • Pam is Greater than or Equal to 16.
    Solve this to show an inequality for Amanda's age.
    • u - 7 >= 16
      • Substitute (u-7) for p as they are equal.
    • (u - 7) + 7 >= 16 + 7
    • u >= 23
      • solving for u.
    For anyone that couldn't follow what Brit was saying. :)

    Regards,
    SB
     
  7. Tahir2

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    Thanks for your help BRiT and Silent Buddha, my daughter is looking over your answers with a new insight. Hopefully she can figure out the rest for herself.
     
  8. Tahir2

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    My daughter looked at the answers and said that BRiT processed Jill's inequality rather than Tom's therefore not answering the question. :)
     
  9. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    She is correct. As I disclaimered, lack of sleep. :lol:
     
  10. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    Tim is half Jill's age, Jill is b years.
    a) write an expression for Jill's age.
    b) Tim is 14 years old or younger, show this as an inequality.
    c) Show an inequality for Jill's age.

    ---
    [ Turning the statements into math statements ]
    Tim = 1/2 * Jill
    Jill = b

    Part a)
    Therefore we need to rework it somewhat to get statement for Jill
    Tim = 1/2 * b
    [ multiply both sides by 2 ]
    2 * Tim = b
    [ restructure equation to be centered on Jill ]
    B = 2 * Tim

    a) b = 2 * Tim

    Part b)
    Turn the statment of Tim being 14 or youngerto an equation
    Tim <= 14

    Part c)
    We have 2 statements that I think can be combined using substitution property
    B = 2 * Tim
    And
    Tim <= 14

    Produces
    b = 2 * 14 [ at the greatest age of Tim who is 14 or younger ]

    So if he's younger then Jills age becomes
    b <= 2 * 14

    Which reduces down to
    b <= 28


    .....

    Seems like some parts end up the same, just maybe needed to flip the one equation to have Jill on the left side?
     
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  11. Davros

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    what is an equality?
     
  12. tangey

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    Yeah, I thought I was the only only that didn't recognise that term.

    Also
    Seems a very vague question. Solve WHAT ?
     
  13. zed

    zed
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    Yeah what is inequality? Perhaps I understand it wrong been many years since I was in school maths
    Looking on dictionary
    which is what I thought it meant, yet Brit & Silent_Buddah are using <= , >= (≤ , ≥)
    which to me is certainly not an inequality, but like I said been many years so perhaps they are right
     
  14. Tahir2

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  15. BRiT

    BRiT (>• •)>⌐■-■ (⌐■-■)
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    Equality is: =
    Any other mathematical sign is an inequality, includes: <, <=, >, >=, != or <>


    At least howI parsed it.
     
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  16. orangpelupa

    orangpelupa Elite Bug Hunter
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    How about

    >_<
    \(^_^)/

    ...

    Sorry.. I just can't help but think of those after reading your examples
     
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  17. zed

    zed
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    yes I agree
    now I agree with <,>,!= (but not >=,<=)

    x = 3, y = 3
    x >= y (yes I agree this is true)
    x is an inequality to y (but saying this just seems wrong to me )

    you could be correct,( been a long time since I looked at this)

    x >= x
    x is an inequality to x, x is an equality to x (so both statements are correct?)
     
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  18. smw

    smw
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    < and > are known as strict inequalities in contrast to ≥ and ≤ which are not strict, but all of them are inequalities.
    While x ≥ x may seem strange, this is actually quite useful :) If you prove that x ≥ y and y ≥ x, this means that x = y. Also, if you are testing some assertion and you end up with something like x > y and y > x (i.e. strict), then your assertion is wrong (this can be used e.g. in counterexamples).
     
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  19. zed

    zed
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    Yes I agree with all that, my point is about calling them 'inequalities' eg
    3 is an inequality of 3
    To me that just sounds wrong, perhaps as a math term its correct, I don't know but I'll take yours words for it

    A/ 3 is an equality of 3
    B/ 3 is an inequality of 3
    both A & B are correct

    Are there any rational numbers that are not an inequality to any other rational number?
    i.e. its a statement thats always true (though perhaps not for irrational numbers, though perhaps its also true for these as well?)

    I'ld feel better about it by there being 3 terms
    equality, quasequality (or something), inequality
    I suppose you could argue 'strict inequality' but thats messy
     
    #19 zed, Jan 17, 2018
    Last edited: Jan 17, 2018
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