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Difference in heights

  1. Jan 2, 2016 #1
    1. The problem statement, all variables and given/known data

    Pritesh is taller than Davina who is taller than Alicia. The difference in height between Pritesh and Davina is the same as the difference in height between Davina and Alicia. The total of their heights is 300 cm. How tall is Davina?

    2. Relevant equations

    Now trial and error gives me Alicia = 50cm, Davina = 100cm and Pritesh = 150cm as the difference between them is 50cm

    3. The attempt at a solution

    How could I do this problem using only algebra, rather than what I did with trial and error?
     
  2. jcsd
  3. Jan 2, 2016 #2

    berkeman

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    Staff: Mentor

    Maybe P+D+A = 300

    P-D = D-A

    Are those two equations enough to get the solution? :smile:
     
  4. Jan 2, 2016 #3
    P = 2D - A

    So substituting gives
    2D - A + D + A = 300
    3D = 300
    D = 100

    How do I get P and A?
     
  5. Jan 2, 2016 #4
    Hi, let's write these info:

    P+A+D= 300
    D-P=A-D

    You need D

    Look at the second equation, you can write it as: 2D= P+A , that's amazing

    Look at the first : (P+A)+D= 300

    Can you see it?
     
  6. Jan 2, 2016 #5
    You can't, you need another equation, but you only need D
     
  7. Jan 2, 2016 #6
    D-100=A-100

    So D = A which is wrong??
     
  8. Jan 2, 2016 #7

    berkeman

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    Staff: Mentor

    Just re-check your algebra... :smile:
     
  9. Jan 2, 2016 #8
    P-D = D-A
    so
    P - 100 = 100 - A
    P = 200 - A
    A = 200 - P

    Is this correct?
     
  10. Jan 2, 2016 #9

    phinds

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    Gold Member
    2016 Award

    Does it give the right answer?
     
  11. Jan 3, 2016 #10

    Samy_A

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    Science Advisor
    Homework Helper

    So Davina is 100 cm tall, that is correct.
    You don't have enough information to answer that question. That's why you are only asked how tall Davina is.
     
  12. Jan 3, 2016 #11
    Can you remember a technique that allows you to deal with more than one unknown quantity, and can you recognize the quantity you do not need to answer this question?

    Hint: look at your algebra, it'll be easier to think about this algebraically than from just reading the problem text (which is what you're asking for, correct?).
     
  13. Jan 3, 2016 #12

    HallsofIvy

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    Staff Emeritus
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    Let P be the Pritesh's height, in cm, D be Davina's height in cm., and A be Alicia's height in cm.

    So P- D= D- A.

    And A+ D+ P= 300. That give two equations, P- D= D- A and A+ D+ P= 300 to solve for three unknowns. That is not enough information. We need one more equation. We Could write P- D- A as 2D= P+ A and replace "P+ A" in the second equation by 2P to get 2D+ D= 3D= 300 to get D= 100. But putting D= 100 in either of the two equations gives P- 100= 100- A so that A+ P= 200.

    Yes, that is one solution. But taking, say, A= 40, P= 200- 40= 160 also satisfies A+ P= 200 so also satisfies "P- D= 160- 100= 60" and "D- A= 100- 40= 60". Or taking A= 25, P= 200- 25= 175, which also satisfies A+ P= 200 as well as "P- D= 175- 100= 75" and "D- A= 100- 25= 75".

     
  14. Jan 4, 2016 #13
    Thank you everyone, I have understood
     
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