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29 May, 03:22

If a+b+c=8, b+c=9, c+a=11 then what is the average of a, b and c.

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  1. 29 May, 07:18
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    First, we solve for all the variables. We use the system of equations. I will be making the equations b+c=9 and c+a=11 to have b=? and a=? and plug it in to the overall equation.

    b+c=9

    b=9-c

    c+a=11

    a=11-c

    a+b+c=8 ← Plug in the above equations for their corresponding variable.

    (11-c) + (9-c) + c=8 ← Remove parentheses

    11-c+9-c+c=8 ← Combine like terms

    20-c = 8

    20 = 8 + c

    20 - 8 = c

    12 = c

    Next, we plug c in to the other two equations to find a and b:

    b + c=9

    b+12=9

    b=-3

    c+a=11

    12+a=11

    a = - 1

    Then, we have to find the average. There are three numbers, so we add up a, b, and c and we divide by 3.

    (12 + - 3 + - 1) / 3 = (12-3-1) / 3 = 8/3 is the average
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