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Math Help - Fraction Question - Urgent

  1. #1
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    Fraction Question - Urgent

    Linda is 9/10 as tall as patrick and 3/4 as tall as Ali. If the total height of the 3 pupils is 418.5 cm, how much taller is Ali than Patrick? Please help me and tell me how you get the answer step by step. Thanks
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    Quote Originally Posted by aznmartinjai View Post
    Linda is 9/10 as tall as patrick and 3/4 as tall as Ali. If the total height of the 3 pupils is 418.5 cm, how much taller is Ali than Patrick? Please help me and tell me how you get the answer step by step. Thanks
    We have three people, with three unknown heights. Call the respective heights of Linda, Patrick, and Ali h_1,\,h_2,\text{ and }h_3.

    Since Linda's height is \frac9{10} that of Patrick, we have

    h_1 = \frac9{10}\cdot h_2.

    Similarly, for Linda and Ali we have

    h_1 = \frac34\cdot h_3.

    But we further know that the sum of all three heights is 418.5 cm. This gives:

    h_1 + h_2 + h_3 = 418.5\text{ cm}.

    You now have three equations with three unknowns. Can you solve this system?
    Last edited by Reckoner; July 5th 2008 at 03:59 PM.
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  3. #3
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    Let L = Linda,  P = Patrick, A = ali.
    L=\frac{9}{10}P, L = \frac{3}{4}A
    we have
     <br />
P=\frac{10}{9}L, A=\frac{4}{3}L<br />
    P+A+L=418.5
    now just replace the P and  A as expressed with  L above and you'll find the height of Lisa first, then others.
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    i still don't know how to get h2? can you tell me please?
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    Quote Originally Posted by aznmartinjai View Post
    i still don't know how to get h2? can you tell me please?
    If you were able to find h_1 and h_3, then you can simply substitute them into the third equation and solve for h_2.
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    so h1 h3 are the same number?
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    Quote Originally Posted by aznmartinjai View Post
    so h1 h3 are the same number?
    No, they should be distinct. What values did you get? Show some of your work.
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    i dont know how you get h1....
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    h1 = 9/10 x 50 = 45 and h2 = 3/4 x 60 = 45 until now you say thier distince. I wonder if you can tell me so i can study it and better understand the problem..
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  10. #10
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    Quote Originally Posted by aznmartinjai View Post
    i dont know how you get h1....
    Substitute equation (2) into equation (1) to get h1 in terms of h3.
    Substitute this expression for h1 and the expression for h2 into equation (3) and solve for h3.
    Use the value of h3 to get the value of h2.
    Use the value of h2 to get the value of h1.
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    Quote Originally Posted by aznmartinjai View Post
    h1 = 9/10 x 50 = 45 and h2 = 3/4 x 60 = 45 until now you say thier distince.
    Hold on, I just realize that I misread the problem. I thought it said Patrick (not Linda) was \frac34 as tall as Ali. Let me correct my post.

    Edit: Alright, the values should still be distinct. Where did you get the 50 and the 60 in your two equations above?
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  12. #12
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    is this right?

    L = 121.5 cm
    P = 135 cm
    A = 162 cm

    A - P = 27 cm
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    Quote Originally Posted by aznmartinjai View Post
    is this right?

    L = 121.5 cm
    P = 135 cm
    A = 162 cm

    A - P = 27 cm
    Correct!
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  14. #14
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    ty recknor and also what was your step by step to the answer? i also want to see how you did it
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    Quote Originally Posted by aznmartinjai View Post
    ty recknor and also what was your step by step to the answer? i also want to see how you did it
    From the three equations in my first post (now corrected), I just used simple substitution to solve the system: I solved the first two equations for h_2 and h_3, respectively, and then substituted into the third equation, which could then be solved for h_1.
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