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Math Help - The average of A and B is 2.5...

  1. #1
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    The average of A and B is 2.5...

    The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by ceasar_19134 View Post
    The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.
    if the average of A and B is 2.5, then

    (A + B)/2 = 2.5
    => A + B = 5

    if the average of B and C is 3.8, then
    (B + C)/2 = 3.8
    => B + C = 7.6

    if the average of A and C is 3.1, then
    (A + C)/2 = 3.1
    => A + C = 6.2

    thus we have three simultaneous equations:

    A + B = 5 ......................(1)
    B + C = 7.6 ....................(2)
    A + C = 6.2 ....................(3)

    subtract eqaution (1) from (3), we get:

    C - B = 1.2 ..............(4) = (3) - (1)
    B + C = 7.6 ...............(2)

    add these two equations, we get:
    2C = 8.8
    so C = 4.4

    but A + C = 6.2 ...............(3)
    so A + 4.4 = 6.2
    so A = 6.2 - 4.4 = 1.8

    but A + B = 5 ..................(1)
    so 1.8 + B = 5
    so B = 5 - 1.8 = 3.2

    so we have
    A = 1.8, B = 3.2, and C = 4.4
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  3. #3
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    Quote Originally Posted by ceasar_19134 View Post
    The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.
    1. A+B=5

    2. B+C=7.6

    3. A+C=6.2

    Equation 3 minus equation 1 gives:

    4. C-B=1.2

    Equation 2 plus equation 4 gives:

    5. 2C=8.8

    So C=4.4, substitute this into 3 gives A=1.8, and into 2 gives B=3.2

    RonL
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  4. #4
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    Hello, ceasar_19134!

    I found another method . . . It's kind of devious and I don't recommend it.
    . . But I thought I'd show it to you anyway.


    The average of A and B is 2.5, the average of B and C is 3.8,
    and the average of A and C is 3.1. . Find A, B, and C.

    We have: .(A + B) .= .2.5 . . A + B .= .5.0 .[1]
    . . . . . . . .(B + C) .= .3.8 . . B + C .= .7.6 .[2]
    . . . . . . . .(A + C) .= .3,1 . . A + C .= .6.2 .[3]

    Add the three equations: .2A + 2B + 2C .= .18.8 . . A + B + C .= .9.4 .[4]


    Subtract [1] from [4]: .A + B + C .= .9.4
    . . . . . . . . - - - . . . . .A + B . - . .= .5.0
    and we get: .C = 4.4


    Subtract [2] from [4]: .A + B + C .= .9.4
    . . . . . . . . - - . . . . . . . . .B + C .= .7.6
    and we get: .A = 1.8


    Subtract [3] from [4]: .A + B + C .= .9.4
    . . . . - . . - - . . . . . . .A . .+ . .C .= .6.2
    and we get: .B = 3.2

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