Question 474940
The average age of 8 men is increased by 2, when two men of 21 yrs and 23 yrs are replaced by two new men.
what is the average of ages of two new men
:
Total age of the new men is 44
:
Let a = total age of the 6 men that are unchanged
then
(a+44) = total age of the 8 men originally
and
{{{(a+44)/8}}} = original average age
:
let b = total age of the 2 new men
then
{{{(a+b)/8}}} = new average age
:
the equation for the given statement
:
New average = old average + 2
{{{(a+b)/8}}} = {{{(a+44)/8}}} + 2
multiply by 8
a + b = a + 44 + 16
Subtract a from both sides
b = 44 + 16
b = 60 is the total age of the two new men
and
{{{60/2}}} = 30 is the average age of the two new men
:
:
We can check this with real numbers if we can find a, but it's on both sides of
the equation so let's just assume a=124, (the total age of the 6 men)
{{{(124+60)/8}}} = {{{(124+44)/8}}} + 2
{{{184/8}}} = {{{168/8}}} + 2
23 = 21 + 2