TITLE: Finding the ages of father and son without using algebraic equations
QUESTION [0 upvotes]: The question that I am about to request for your help is almost similar to the one that appears here.
However, I am stumped by the wording of the question as it appears in the pages of an old math book from where I picked it up.

Five years ago the sum of the ages of a father and his son was 40
years. Five years hence, the age of the father will be 3 times the age
of his son. Find their present ages.

The solution is given thus (without using variables):

The sum of the present ages of the father and his son = $40+5+5=50$
years.
5 years hence the sum of their ages will be = $50+5+5=60$ years.
But by the question, this sum is 4 times the age of the son; Therefore, 5 years hence, the age of the son will be = $60 / 4 = 15$
years and that of his father $60-15=45$ years.
Therefore, the present ages of the father and son are $45-5=40$, and
$15-5=10$ years, respectively.

The part of the solution that I cannot understand is how is the statement - But by the question, this sum is 4 times the age of the son - arrived at?
Any help will be much appreciated.

REPLY [1 votes]: It's the same as dividing $60$ (cookies, for example) into the ratio $3:1$.
The sum of the parts, which are all equal, is $60$. Thus $4 \ \text{parts} = 60 \implies 1 \  \text{part} = 15$, and one part is the same as the son's age. Hence the son's age must be $15$ at the given time.
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