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help with a simple math question

Discussion in 'DAT Discussions' started by rcwha, Jun 22, 2008.

  1. rcwha

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    I'm having trouble setting up these kind of math questions:

    Sally is 4/5 as old as her sister Jane. Their brother Dick's age is 1/3 more than Jane's. If Dick is 20, how old is Sally?

    Know here is the explanation from kaplan....

    This is a relatively easy problem. You just have to be careful when you set up your equations. Let's
    let S be Sally's age, in years, J be Jane's age, in years, and D be Dick's age, in years. We know that Sally
    is
    4
    5
    as old as Jane, thus S = 4/5
    J . We know that Dick's age is1/3
    more than Jane's age, thus Dick's age is 4/3
    times Jane's age or D = 4/3j

    J . We are given that Dick's age is 20. We have 20 = 4/3
    J . To get J, we
    multiply both sides of this equation by3/4
    , so J = 3/4
    D = 3
    4
    (20) = 3 × 5 = 15, therefore Jane is 15 years old.
    Now we want to find Sally's age. We know that S = 4
    5
    J meaning that Sally's age is
    4
    5
    of Jane's age. We
    know that Jane's age is 15, therefore Sally's age is
    4
    5
    of 15, or 12. Sally's age is 12 and that is answer
    choice C.




    The part im stuck at is when they say We know that Dick's age is1/3
    more than Jane's age, thus Dick's age is 4/3
    times Jane's age or D = 4/3j

    How do you get D= 1/3 + J (i don't know if this set up is even right) to D=4/3J?
     
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  3. DentalDeac

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    Ok. Since they said that Dick age is 1/3 more than Janes age, Dicks age is Janes age (J) + 1/3 of Jane's age (1/3J)

    D = 1/3J + J therefore D = 4/3J
     
  4. rcwha

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    k thanks, I guess i didn't interpret the statement " Dick's age is 1/3 more than Janes" correctly... I mean how do you get 1/3j + j = d from that statement?
     
  5. DentalDeac

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    Honestly I'm not sure if there is really any other way to say it. Dick's age, D, is 1/3 more than Jane's (J). So in order for this to work, you have to take Jane's age J and add 1/3 of Jane's age to get Dick's age, because its 1/3 MORE not just 1/3 of her age.
     
  6. rcwha

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    If it was a whole number, say 2, would you set it up differently? If it said Dick's age, D, is 2 more than Jane's (J)?
     
  7. Mstoothlady2012

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    let's say Jane's age is J

    then Dick's age would be D = J + 2
     
  8. rcwha

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    Why couldn't they just say dick's age is 1/3 more than 1/3 jane's age?

    That makes more sense, doesn't it?
     
  9. Mstoothlady2012

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    no then the equation would be...

    D = 1/3 + 1/3J
     
  10. rcwha

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    k k I confused myself...ur right toothlady

    But you guys are see what im trying to say right? there's gotta be a better way to write it

    That makes more sense, doesn't it?
     
  11. Mstoothlady2012

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    Actually, I think the problem is worded fine. These are word problems, so they are not suppose to give you straightforward numbers, because then it wouldn't be called word problems. Just read each sentence and try to convert it into equation, and you should have no problem solving. It needs practice though!
     
  12. Streetwolf

    Streetwolf Ultra Senior Member
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    No that is exactly what it should say. You need to practice converting english into math. Pay attention to key words such as 'is', 'more than', 'less than', 'times', and so forth.

    Go through this step by step. 'Their brother' is useless information. 'Dick's age' is important because this refers to the variable 'D' that you've created. 'is' is important because it represents the EQUAL sign.

    Now you have 'D ='.

    '1/3 more than Jane's [age]'. It might help to put 'age' in that even though they left it out. It should be implied. How do you put this in math symbols?

    Obviously there's a 1/3 involved and a J involved. If you took it literally you'd write out 1/3 + J. But that makes no sense because 1/3 HAS NO UNITS. This is very important because you cannot add two things without the same units. You have to take a step back and recognize that 1/3 refers to a portion of Jane's age. So you have J which is Jane's age. And you want Dick to be this age plus 1/3 of this age. So you do 1/3 J + J = 4/3 J. And so D = 4/3 J.

    If instead the problem read as follows:

    Dick is two years older than Jane

    Then you would have D = 2 + J.

    I don't think they would say 'Dick's age is 2 more than Jane's.
     
  13. rcwha

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    Thanks for the help guys!
     

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