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Math Help - Find the values of S1 & S2? Need help.

  1. #1
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    Question Find the values of S1 & S2? Need help.

    Okay... so here's the deal

    It's given

    S1 + S2 = 16 ---------- Eqn. (1)

    And S1 X S2 = 3(S1 + S2) = 3 X 16 = 48 -------- Eqn. (2)

    The answers are S1 = 12 & S2 = 4. It says solving the eqns (1) & (2)

    I don't understand how the answers can be ontained by solving (1) & (2). Exactly how can the eqns be solved??

    I tried squaring both the sides in Eqn. (1). But that just brings the the square term which I need to eliminate. The way I did gave me two answers for each of S1 & S2.

    However, the answers are only two, not four.

    Please help.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by arijit2005 View Post
    Okay... so here's the deal

    It's given

    S1 + S2 = 16 ---------- Eqn. (1)

    And S1 X S2 = 3(S1 + S2) = 3 X 16 = 48 -------- Eqn. (2)

    The answers are S1 = 12 & S2 = 4. It says solving the eqns (1) & (2)

    I don't understand how the answers can be ontained by solving (1) & (2). Exactly how can the eqns be solved??

    I tried squaring both the sides in Eqn. (1). But that just brings the the square term which I need to eliminate. The way I did gave me two answers for each of S1 & S2.

    However, the answers are only two, not four.

    Please help.
    Solve the first equation for, say, S2:
    S_2 = 16 - S_1

    Now put that into the second equation:
    S_1 \cdot (16 - S_1) = 3(S_1 + (16 - S_1) ) = 48

    This is a quadratic equation. So expand this out and solve the quadratic. I get two sets of solutions:
    S_1 = 12,~S_2 = 4~\text{and}~S_1 = 4,~S_2 = 12

    -Dan
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  3. #3
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    Quote Originally Posted by topsquark View Post
    Solve the first equation for, say, S2:
    S_2 = 16 - S_1

    Now put that into the second equation:
    S_1 \cdot (16 - S_1) = 3(S_1 + (16 - S_1) ) = 48

    This is a quadratic equation. So expand this out and solve the quadratic. I get two sets of solutions:
    S_1 = 12,~S_2 = 4~\text{and}~S_1 = 4,~S_2 = 12

    -Dan
    Thanks for your reply Dan.

    Well, yeah, this is a quadratic equation. But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set, which is why I'm getting confused.

    See, it's about the specific gravities of two substances in an alloy, where S1 & S2 represent the sp. gravities of the 1st & 2nd substances respectively. Now one substance can't have to sp. gravities, can it?

    Is there any other way you can get only one set of solutions?
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  4. #4
    A Plied Mathematician
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    Without knowing more about the problem, you can't rule out one of the possibilities. Do you know what the two substances in the alloy are?
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  5. #5
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    Quote Originally Posted by arijit2005 View Post
    But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set, which is why I'm getting confused.
    IF one set only, then problem MUST state: where S1 > S2
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  6. #6
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    No.. I'm not told what the substances are....
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  7. #7
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    Quote Originally Posted by Wilmer View Post
    IF one set only, then problem MUST state: where S1 > S2
    Well, that condition is not given either...

    Anyways..

    Thank you all for taking the time to respond..
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  8. #8
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    Quote Originally Posted by arijit2005 View Post
    But there's only one set of solutions [S1 = 12 & S2 = 4]. Had there been two sets of solutions, as you have already shown, shouldn't they have been mentioned in the solution book? But there's only 1 set,.....
    REPEATING: IF there's only ONE set of solutions in "the book",
    then "the book" SHOULD specify S1 > S2.
    If x and y are positive integers > 0 and x + y = 3, then if there is ONLY one solution,
    x > y or y > x MUST be specified
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