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I need to figure out some averages for some javascript I'm writing. The data I have is:

  • I know the average of $a$, $b$ and $c$.
  • I know the value of $c$.
  • I do not know the values of $a$ and $b$.

What I need to know is the average of $a$ and $b$. It must be possible, but I can't figure it out.

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Hint: We have $$ 3\cdot\frac{a+b+c}{3}-c=a+b. $$

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Let $$\frac{a+b+c}{3}=k$$ but k is a known value.

Then $$a+b+c=3k$$. This implies $$a+b=3k-c. \cdot\cdot\cdot (1)$$

Now, suppose the average of a and b is $m$ an unknown value.

Then $$\frac{a+b}{2}=m$$Thus, $$a+b=2m$$. Therefore from $(1)$ $$3k-c=2m$$. From this $$m=\frac{3k-c}{2}$$ At last you can put the known values of $k$ and $c$ to get your result.

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Clear and simple. – NoChance Oct 29 '11 at 16:25

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