# Problem of the Day

If , , and , what is the average of , , and ?

A. 4
B. 6
C. 8
D. 10
E. 12

A. 4

See the Solution

### Solution

[latexpage]

The average of $a$, $b$, and $c$ is $\displaystyle \frac{a+b+c}{3}$. If we can find the value of $a+b+c$ we can plug it in to this expression to find the answer. Note that we don’t have to find the individual values of $a$, $b$, and $c$, just their sum. The easiest way to do this is to add all three given equations together. This gives us $2a+2b+2c=24$. Dividing both sides of this equation by $2$ gives us $a+b+c=12$. Thus, the average of $a$, $b$, and $c$ is $4$.

This trick of adding all of the equations together comes up frequently on standardized tests. Keep it in mind and look for places you can use it when there is no other obvious way to proceed.