How to get the average of $a$, $b$ when all you know is the average of $a,b,c$ and the value of $c$?

Question

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.

Answer 1

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

Answer 2

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.