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Thread: Partial variation

  1. #1
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    Partial variation

    Hi, I have an exam in two days involving a few areas of math and unfortunately I have NOT studied for it at all (not something I usually do but I had other subjects that needed to be prioritised). Here is one of the problems I am having trouble with. If it's okay, I'd like to see a complete worked out example for future reference.

    If A varies partly with B, and A=15 when B=2, and A= 27 when B= 5, find A when B=10


    And I emphasize, any help will be strongly appreciated!
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  2. #2
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    ....partly with B.
    So B is part of a quantity.
    Let that quantity be (B +u).
    Hence, A = k(B +U) -----------------(i)
    where k = constant of variation

    When A = 15, and B = 2
    15 = k(2 +u) --------------(1)

    When A = 27, and B = 5
    27 = k(5 +u) --------------(2)

    Solve (1) and (2) simultaneously and you'd get
    u = 7/4
    and k = 4

    So, when B = 10,
    A = 4(10 +7/4)
    A = 47 -----------------answer.
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  3. #3
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    What do you mean solve (1) and (2) simultaneously? I don't understand...How did you get 7/4?
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  4. #4
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    Quote Originally Posted by Joker37 View Post
    What do you mean solve (1) and (2) simultaneously? I don't understand...How did you get 7/4?
    You have not encountered yet solving equations simultaneously?
    Incredible.

    Anyway, "solving simultaneously" here means solving for the values of the unknowns that will satisfy the many equations simultaneously. Or, the k of one equation is also the same k of the other equation. The u of one equation is the equal to the u of the other equation. Etc...

    Or, you find the intersection points of the many equations.

    :-), I think you're more lost now than before you read the above.

    15 = k(2 +u) --------------(1)
    27 = k(5 +u) --------------(2)

    15 = 2k +uk ------------(1a)
    27 = 5k +uk ------------(2a)

    To eliminate uk, subtract (1a) from (2a),
    12 = 3k
    k = 12/3 = 4 ---------**

    Substitute that into, say, (1),
    15 = 4(2 +u)
    15 = 8 +4u
    15 -8 = 4u
    u = 7/4 -----------**
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