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Math Help - Solving for Variables

  1. #1
    Newbie
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    Solving for Variables

    Okay, so I'm having a difficult time understanding how to solve problems such as


    Solve for B1: A=1/2(B1+B2)h

    Help please!?

    Thanks.
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  2. #2
    Junior Member
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    Jun 2009
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    Your first step should be to make B1 not be in the denominator of a fraction. Either take the reciprocal of each side or multiply both sides by that denominator. You could multiply both sides just by (B1 + B2) also. In the end, you'll end up with the same answer regardless.

    edit: I'm assuming 2(b1 + b2)h are all in the denominator, though it's a little ambiguous the way you've written it.
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  3. #3
    MHF Contributor

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    It may help to think of "undoing" what has been done to the variable.

    Here, the equation you have is, I suspect, A= (\frac{1}{2})(B_1+ B_2)h. That is NOT what 1005 assumed- as he said, what you wrote is ambiguous. I am assuming only the "2" is in the denominator because that looks to me like the formula for the area of a trapezoid.

    Suppose you were given a value of B_1 and the other things on the right and wanted to find A, what would you do? The formula tells you what do do- first add B_1 and B_2 (because they are in parentheses) then multiply by h and then multiply by 1/2 (the order of those two is not really important). To solve for B_1, you do the opposite of each step and in the opposite order! That is first, divide by 1/2 (which is the same as multiply by 2) and, of course, do the same thing to both sides of the equation: multiplying both sides of A= (\frac{1}{2})(B_1+ B_2)h by 2 gives 2A= 2(\frac{1}{2})(B_1+ B_2)h= (B_1+ B_2)h. Now divide both sides by h: [tex]\frac{2A}{h}= (B_1+ B_2)h/h= B_1+ B_2. Finally, since the first thing you woud do in calculating A would be to add B_1 and B_2, the last thing you do in solving for B_1 is subtract B_2 from both sides: \frac{2A}{h}- B_2= (B_1+ B_2)- B_2= B_1.
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  4. #4
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    Thank you all! I understand now
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