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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.

stickynotememo
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Fruitjam
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2 Answers2

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The sum is four times the age of the son because it is the son's age plus the father's age, which is three times the son's age, making four times the son's age.

If you don't mind "breaking the law" and using algebraic equations, you can go wild as follows and solve in a jiffy: $$\sum=F+S=3S+S=4S,$$ where $F=3S$ is the father's age and $S$ is the son's age.

Suzu Hirose
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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.

Toby Mak
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