Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

If (3.44 + x)/2 = 3.68 what is x when x is 55% weighted and 3.44 is 45% weighted?

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  • 1 month ago

    To get 3.68, that's an average, meaning equal weighting.  So the answer will be different.

    Let's do the math showing the 50% equal weighting and show that it's the same as the mean.

    if you add 50% of "x" to 50% of 3.44, you get:

    0.5x + 0.5(3.44)

    Factor out the 0.5:

    0.5(x + 3.44)

    and 0.5 is the same as multiplying by (1/2), so:

    (1/2)(x + 3.44)

    (x + 3.44)/2

    And this is the same as getting an average of two numbers.  So now, instead of using 50%, use 55% and 45%:

    0.55x + 0.45(3.44)

    simplify:

    0.55x + 1.548

    So whatever "x" is will give you a different value for the weight.

    --------------------

    If  you are just needing to know what "x" is based on the given average, then we can solve for that from the original equation:

    (3.44 + x) / 2 = 3.68

    3.44 + x = 7.36

    x = 3.92

    -------

    If we now use this value for "x" in the weighted expression, since 3.92 is larger than 3.44 and it's using a larger weighted amount, the result should be larger than the given average:

    0.55x + 1.548

    0.55(3.92) + 1.548

    2.156 + 1.548

    3.704

    That's then the value of the weighted average, which is larger than the given mean.

  • 1 month ago

    If (3.44 + x)/2 = 3.68, then x = 3.92. You'll have to explain what the rest means. Do you mean the weighted average of 3.44 and x is 3.68 with the weights 45% and 55% respectively?

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