SOLUTION: I was asked to write an equation that models how old in years each of you will be, when your ages add up to 150 years old.The ages are 41, 14, and 57. x=41 which is my age. The equ

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Question 731600: I was asked to write an equation that models how old in years each of you will be, when your ages add up to 150 years old.The ages are 41, 14, and 57. x=41 which is my age. The equation that I came up with is x+(x+16)=150.But I cant explain it.I believe it would go like this 41+(x+16)=150. I think the next step would be finding the x in the parenthesis. 41+(41+16)=150. Im not getting the right answer when solving what am I doing wrong.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bn, 14%2Bn, and 57%2Bn
The sum will be
%2841%2Bn%29%2B%2814%2Bn%29%2B%2857%2Bn%29=150 or 41%2Bn%2B14%2Bn%2B57%2Bn=150
Rearranging and simplifying:
41%2B14%2B57%2Bn%2Bn%2Bn=150
112%2Bn%2Bn%2Bn=150
112%2B3n=150
To solve that equation, the first step is to add -112 to both sides (people call that subtract 112 from both sides).
112%2B3n=150 --> 112%2B3n-112=150-112 --> 3n=38
The next step would be dividing both sides of the equal sign by 3:
3n=38 --> n=38%2F3
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.