Question 731600
The way you define a variable can make the equation easy to formulate or very difficult.
 
I would define as follows
{{{n}}}= number of years until the ages add up to 150.
You could find an equation to calculate {{{n}}} and an expression based on n for the age of each of the 3 persons.
 
In {{{n}}} years your ages will be:
{{{41+n}}}, {{{14+n}}}, and {{{57+n}}}
The sum will be
{{{(41+n)+(14+n)+(57+n)=150}}} or {{{41+n+14+n+57+n=150}}}
Rearranging and simplifying:
{{{41+14+57+n+n+n=150}}}
{{{112+n+n+n=150}}}
{{{112+3n=150}}}
To solve that equation, the first step is to add {{{-112}}} to both sides (people call that subtract {{{112}}} from both sides).
{{{112+3n=150}}} --> {{{112+3n-112=150-112}}} --> {{{3n=38}}}
The next step would be dividing both sides of the equal sign by 3:
{{{3n=38}}} --> {{{n=38/3}}}
That rounds up to 13.
In exactly 12 years the ages would be
41+12=53
14+12=26
57+12=69
Then the sum would be 53+26+69=148.
In exactly 13 years the ages would be
41+13=54
14+13=27
57+13=70
Then the sum would be 54+27+70=151.
To get the sum to be exactly 150 you would have to wait 12 years and then some more months until two of the 3 people have a birthday, but the third one is not yet counted as a year older.
 
STRANGE DETAIL:
However, if the last two birthdays are the same day, you could never add up to 150.
For example, if a woman adopts a newborn boy and a short time later, on her 19th birtday, she has a daughter, then 43 year later,
the mother will be 19+43=63, and
the children will be 43.
Their ages will add up to 62+43+43=148.
Some time after that, the adopted son will have a birthday and the sum will be
62+44+43=149.
The next birthday will be shared by mother and daughter, and then their ages will add up to
63+44+44=151, never having added to 150.