Question

Three numbers are such that when the sum of any two of them is added to half of the third, the results are 210, 198, and 192 respectively. What is the average of the three numbers?

• A. 80
• B. 70
• C. 60
• D. 50

Answer 1

Answer:

A. 80

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

The given conditions are:

$a+b+\frac{c}{2}=210$

$b+c+\frac{a}{2}=198$

$c+a+\frac{b}{2}=192$

Add all three equations:

$\left(a+b+\frac{c}{2}\right)$
$+\left(b+c+\frac{a}{2}\right)$
$+\left(c+a+\frac{b}{2}\right)$
$=210+198+192$

$\frac{5}{2}(a+b+c)=600$

$a+b+c=600\times\frac{2}{5}=240$

The average of the three numbers is:

$\frac{240}{3}=80$