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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• 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.

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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

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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.

• 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?