Question

Three numbers are such that when the average of any two of them is added to the third, the results obtained are 180, 168, and 150, respectively. What is the average of the original three numbers?

• A. 83
• B. 84
• C. 85
• D. 86

Answer 1

Answer:

A. 83

Let the three numbers be (a), (b), and (c).

Given:

$\frac{a+b}{2}+c=180$
$\frac{b+c}{2}+a=168$
$\frac{c+a}{2}+b=150$

Adding all three equations:

$\left(\frac{a+b}{2}+c\right)$
$+\left(\frac{b+c}{2}+a\right)$
$+\left(\frac{c+a}{2}+b\right)$
$=180+168+150$
$\frac{(a+b)+(b+c)+(c+a)}{2}+(a+b+c)=498$
$\frac{2(a+b+c)}{2}+(a+b+c)=498$
$2(a+b+c)=498$
$a+b+c=249$

Therefore, the average of the three numbers is

$\frac{a+b+c}{3}$

$\frac{249}{3}$

$=83$